Problems in Physical Chemistry for JEE

Narendra Avasthi

Chapter 7

Chemical Kinetics and Nuclear Chemistry - all with Video Answers

Educators

Chapter Questions

Problem 1

The differential rate law equation for the elementary reaction $A+2 B \stackrel{k}{\longrightarrow} 3 C$, is :
(a) $-\frac{d[A]}{d t}=-\frac{d[B]}{d t}=\frac{d[C]}{d t}=k[A][B]^{2}$
(b) $-\frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=\frac{1}{3} \frac{d[C]}{d t}=k[A]^{2}[B]$
(c) $-\frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=\frac{1}{3} \frac{d[C]}{d t}=k[A][B]^{2}$
(d) None of these

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Problem 2

The rate of reaction is expressed in different ways as follows:
$+\frac{1}{2} \frac{d[C]}{d t}=-\frac{1}{3} \frac{d[D]}{d t}=+\frac{1}{4} \frac{d[A]}{d t}=-\frac{d[B]}{d t}$
The reaction is:
(a) $4 A+B \longrightarrow 2 C+3 D$
(b) $B+3 D \longrightarrow 4 A+2 C$
(c) $A+B \longrightarrow C+D^{\prime}$
(d) $B+D \longrightarrow A+C$

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Problem 3

In the reaction, $A+2 B \longrightarrow 6 C+2 D$, if the initial rate $-\frac{d[A]}{d t}$ at $t=0$ is $26 \times 10^{-2} \mathrm{M} \mathrm{sec}^{-1}$, what will be the value of $-\frac{d[B]}{d t}$ at $t=0 ?$
(a) $8.5 \times 10^{-2} \mathrm{M} \mathrm{sec}^{-1}$
(b) $2.5 \times 10^{-2} \mathrm{M} \mathrm{sec}^{-1}$
(c) $5.2 \times 10^{-2} \mathrm{M} \mathrm{sec}^{-1}$
(d) $7.5 \times 10^{-2} \mathrm{M} \mathrm{sec}^{-1}$

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Problem 4

For the reaction $2 A \longrightarrow B+3 C ;$ if $-\frac{d[A]}{d t}=k_{1}[A]^{2} ; \quad \frac{d[B]}{d t}=k_{2}[A]^{2} ; \frac{d[C]}{d t}=k_{3}[A]^{2}$
the correct reaction between $k_{1}, k_{2}$ and $k_{3}$ is:
(a) $k_{1}=k_{2}=k_{3}$
(b) $2 k_{1}=k_{2}=3 k_{2}$
(c) $4 k_{1}=k_{2}=3 k_{2}$
(d) $\frac{k_{1}}{2}=k_{2}=\frac{k_{3}}{3}$

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Problem 5

The rate constant of $n^{\text {th }}$ order has units :
(a) litre $^{1-n} \mathrm{~mol}^{1-n} \mathrm{sec}^{-1}$
(b) $\mathrm{Mol}^{1-n}$ litre $^{1-n} \mathrm{sec}$
(c) $\mathrm{Mol}^{1-n^{2}}$ litre $\mathrm{e}^{\mathrm{n}^{2}} \mathrm{sec}^{-1}$
(d) Mole $^{1-n}$ litre ${ }^{n-1} \sec ^{-1}$

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Problem 6

Which of the following statement is incorrect?
(a) Unit of rate of disappearance is $M \mathrm{~s}^{-1}$
(b) Unit of rate of reaction is $M \mathrm{~s}^{-1}$
(c) Unit of rate constant $k$ depends upon order
(d) Unit of $k$ for first order reaction is $\mathrm{Ms}^{-1}$

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Problem 7

Which of the following relation is correct for $k_{f}$ and $k_{b}$ in an equilibrium process that contains equal moles of reactants and products.
(a) $k_{f}=k_{b}$
(b) $k_{f}>k_{b}$
(c) $k_{f}<k_{b}$
(d) we cannot predict

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Problem 8

Listed in the table are forward and reverse rate constants for the reaction
$$
2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)
$$
0
Select the correct statement :
(a) Reaction is exothermic and value of equilibrium constant $\left(K_{\mathrm{cq}}\right.$ ) at $1400 \mathrm{~K}$ is $3.79 \times 10^{-6}$
(b) Reaction is endothermic and value of $K_{e q}$ at $1400 \mathrm{~K}$ is $2.63 \times 10^{5}$
(c) Reaction is exothermic and value of $K_{\text {eq }}$ at $1400 \mathrm{~K}$ is $2.63 \times 10^{5}$
(d) Reaction is endothermic and value of $K_{\mathrm{cq}}$ at $1500 \mathrm{~K}$ is $9.28 \times 10^{4}$

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Problem 9

The rate constant of a reaction depends on
(a) temperature
(b) pressure
(c) extent of reaction
(d) initial concentration of the reactant

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Problem 10

In the following reaction, how is the rate of appearance of the underlined product related to the rate of disappearance of the underlined reactant
$$
\mathrm{BrO}_{3}^{-}(a q)+5 \mathrm{Br}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(l)+3 \mathrm{H}_{2} \mathrm{O}(a q)
$$
(a) $-\frac{d\left[\mathrm{BrO}_{3}^{-}\right]}{d t}=\frac{d\left[\mathrm{Br}_{2}\right]}{d t}$
(b) $-\frac{1}{3} \frac{d\left[\mathrm{BrO}_{3}^{-}\right]}{d t}=\frac{d\left[\mathrm{Br}_{2}\right]}{d t}$
(c) $\frac{-d\left[\mathrm{BrO}_{3}^{-}\right]}{d t}=\frac{1}{3} \frac{d\left[\mathrm{Br}_{2}\right]}{d t}$
(d) None of these

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Problem 11

Consider a reaction $A(g)=$ $\longrightarrow 2 B(g)$. If initial concentration of $A$ is $0.5 M$ then select correct graph.
(a)
(b)
time (in min) time (in $\min$ )
(c)
(d)
time (in min) time (in min)

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Problem 12

Which of the following statements is incorrect?
(a) A second order reaction must be a bimolecular elementary reaction
(b) A bimolecular elementary reaction must be a second order reaction
(c) Zero order reaction must be a complex reaction
(d) First order reaction may be complex or elementary reaction

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Problem 13

The molecularity of a complex reaction given below is :
$$
2 \mathrm{~N}_{2} \mathrm{O}_{5}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)
$$
(a) 1
(b) 2
(c) 3
(d) has no meaning

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Problem 14

Decomposition of $\mathrm{NH}_{4} \mathrm{NO}_{2}(a q)$ into $\mathrm{N}_{2}(g)$ and $2 \mathrm{H}_{2} \mathrm{O}(l)$ is first order reaction. Which of the following graph is correct?
(a)
(b)
(c)
(d)

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Problem 15

Decomposition of HI $(g)$ on Gold surface is zero order reaction. Initially few moles of $\mathrm{H}_{2}$ are present in container then which of the following graph is correct?
(a)
(b)
(c)
(d)

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Problem 16

Consider the plots for the types of reaction
These plots respectively correspond to the reaction orders :
(a) $0,2,1$
(b) $0,1,2$
(c) $1,1,2$
(d) $1,0,2$

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Problem 17

If decomposition reaction $A(g) \longrightarrow B(g)$ follows first order kinetics then the graph of rate of formation $(R)$ of $B$ against time $t$ will be:
(a)
(b)
(c)
(d).

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Problem 18

Consider the plots, given below, for the types of reaction
These plots respectively correspond to the reaction orders:
(a) $0.1 .2$
(b) $1,2,0$
(c) $1,0,2$
(d) None of these

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Problem 19

For a zero order reaction, the plot of conc. $(a-x)$ vs time is linear with
(a) $+$ ve slope and zero intercept
(b) - ve slope and zero intercept
(c) $+$ ve slope and non-zero intercept
(d) - ve slope and non-zero intercept

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Problem 20

What will be the order of reaction for a chemical change having $\log t_{1 / 2}$ vs $\log a ?$ (where $a=$ initial concentration of reactant; $t_{1 / 2}=$ half-life $)$
(a) Zero order
(b) First order
(c) Second order
(d) None of these

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Problem 21

A graph between $\log t_{1 / 2}$ and log a (abscissa), a being the initial concentration of $\mathrm{A}$ in the reaction For reaction $A \longrightarrow$ Product, the
rate law is :
$\begin{array}{lll}\text { (a) } \frac{-d[A]}{d t}=K & & \text { (b) } \frac{-d[A]}{d t}=K[A]\end{array}$
(c) $\frac{-d[A]}{d t}=K[A]^{2}$
(d) $\frac{-d[A]}{d t}=K[A]^{3}$

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Problem 22

Consider the reaction $A \longrightarrow B$, graph between half life $\left(t_{1 / 2}\right)$ and initial concentration (a) of
the reactant is
Hence graph between $-\frac{d[A]}{d t}$ and time will be:

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Problem 23

For the ideal gaseous reaction, the rate is generally expressed in terms of $\frac{d P}{d t}$ instead of $\frac{d C}{d t}$ or $\frac{d n}{d t}$ (where $C=\frac{n}{V}$ is concentration and $n$ the no. of moles). What is the reaction among these three expressions if $T$ and $V$ are constant?
(a) $\frac{d C}{d t}=\frac{d n}{d t}=\frac{d P}{d t}$
(b) $\frac{d C}{d t}=\frac{1}{V} \frac{d n}{d t}=\frac{1}{R T}\left(\frac{d P}{d t}\right)$
(c) $R T \frac{d C}{d t}=\frac{d n}{d t}=\frac{d P}{d t}$
(d) None of these

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Problem 24

$$
A_{2}+B_{2} \longrightarrow 2 A B ; \text { R.O.R. }=k[A]^{a}[B]^{b}
$$
Order of reaction with respect to $A_{2}$ and $B_{2}$ are respectively:
(a) $a=1, b=1$
(b) $a=2, b=0$
(c) $a=2, b=1$
(d) None

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Problem 25

For a reaction the initial rate is given as: $R_{0}=k[A]_{0}^{2}[B]_{0}$ by what factor, the initial rate of reaction will increase if initial concentration of $A$ is taken $1.5$ times and of $B$ is tripled?
(a) $4.5$
(b) $2.25$
(c) $6.75$
(d) None of these

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Problem 26

For $A_{(s)}+B_{(s)} \longrightarrow C_{(s)} ;$ rate $=k[A]^{1 / 2}[B]^{2}$, if initial concentration of $A$ and $B$ are increased by factors 4 and 2 respectively, then the initial rate is changed by the factor:
(a) 4
(b) 6
(c) 8
(d) None of these

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Problem 27

Reaction $A \rightarrow B$ follows second order kinetics. Doubling the concentration of $A$ will increase the rate of formation of $B$ by a factor of :
(a) $1 / 4$
(b) $1 / 2$
(c) 2
(d) 4

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Problem 27

Reaction $A \rightarrow B$ follows second order kinetics. Doubling the concentration of $A$ will increase the rate of formation of $B$ by a factor of :
(a) $1 / 4$
(b) $1 / 2$
(c) 2
(d) 4

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Problem 28

The value of rate constant for the written reaction is:
(a) $2.5 \times 10^{-4}$
(b) $2.5 \times 10^{-2}$
(c) $1.25 \times 10^{-2}$
(d) None of these

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Problem 29

Above given question, the value of rate constant for appearance of $A B(g)$ is :
(a) $2.5 \times 10^{-4}$
(b) $2.5 \times 10^{-2}$
(c) $1.25 \times 10^{-2}$
(d) None of these

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Problem 30

The following data pertain to reaction between $\mathrm{A}$ and $\mathrm{B}$.
$\begin{array}{lccc}\text { S. No } & {[\mathrm{A}]} & {[\mathrm{B}]} & \text { Rate } \\ & \text { mol. } \mathrm{L}^{-1} & \text { mol. } \mathrm{L}^{-1} & \mathrm{~mol} . \mathrm{L}^{-1} \mathrm{sec}^{-1} \\ \mathrm{I} & 1 \times 10^{-2} & 2 \times 10^{-2} & 2 \times 10^{-4}\end{array}$
II $2 \times 10^{-2} \quad 2 \times 10^{-2} \quad 4 \times 10^{-4}$
III $2 \times 10^{-2} \quad 4 \times 10^{-2} \quad 8 \times 10^{-4}$
Which of the following inference(s) can be drawn from the above data
(a) Rate constant of the reaction $10^{-4}$
(b) Rate law of the reaction is $k[A][B]$
(c) Rate of reaction increases four times on doubling the concentration of both the reactant, Select the correct answer codes
(a) a $\mathrm{b}$ and $\boldsymbol{c}$
(b) $\mathrm{a}$ and $\mathrm{b}$
(c) $\mathrm{b}$ and $\mathrm{c}$
(d) $c$ alone

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Problem 31

The unit of rate constant of elementary reaction depends upon the :
(a) temperature of the reaction
(b) concentration of reactant
(c) activation energy of the reaction
(d) molecularity of the reaction

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Problem 32

\begin{aligned}
&\text { Select the rate law that corresponds to the data shown for the reaction } A+B \longrightarrow C \\
&\begin{array}{llcc}
\text { Exp. } & \text { [A] } & \text { [B] } & \text { Rate } \\
1 . & 0.012 & 0.035 & 0.10 \\
2 . & 0.024 & 0.070 & 0.80 \\
3 . & 0.024 & 0.035 & 0.10 \\
4 . & 0.012 & 0.070 & 0.80 \\
\text { (a) Rate }=k[B]^{3} & \text { (b) Rate }=k[B]^{4} & \text { (c) Rate } k=[A][B]^{3} & \text { (d) Rate }=k[A]^{2}[B]^{2}
\end{array}
\end{aligned}

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Problem 33

An elementary reaction between $A$ and $B$ is a second order reaction. Which of the followng rate equations must be correct?
(a) $r=k[A]^{2}[B]^{0}$
(b) $r=k[A]^{3 / 2}[B]^{1 / 2}$
(c) $r=k[A]^{0}[B]^{2}$
(d) $r=k[A][B]$

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Problem 34

If ' $a$ ' is the initial concentration of the reactant, the half-life period of the reaction of $n^{\text {w }}$ order
is inversely proportional to :
(a) $a^{n-1}$
(b) $a^{n}$

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Problem 35

Which of the following expressions is correct for zero order and first order respectively [where $a$ is initial concentration]?
(a) $t_{1 / 2} \propto a ; t_{1 / 2} \propto \frac{1}{a}$
(b) $t_{1 / 2} \propto a ; t_{1 / 2} \propto a^{0}$
(c) $t_{1 / 2} \propto a^{0} ; t_{1 / 2} \propto a$
(d) $t_{1 / 2} \propto a ; t_{1 / 2} \propto \frac{1}{a^{2}}$

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Problem 36

The unit of rate constant of zero order and first order chemical reactions are respectively:
(a) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}, \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
(b) $\mathrm{s}^{-1}, \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~s}^{-1}$
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}, \mathrm{~s}^{-1}$
(d) None of these

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Problem 37

The units of rate of reaction and rate constant are same for a :
(a) zero order reaction
(b) first order reaction
(c) second order reaction
(d) third order reaction

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Problem 38

$\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \stackrel{\mathrm{H}^{+}(a q)}{\longrightarrow} \mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) .$ What type of reaction .c.
is this?
(a) Unimolecular elementary
(b) Pseudo first order
(c) Zero order
(d) Second order

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Problem 39

When ethyl acetate was hydrolysed in presence of $0.1 \mathrm{M} \mathrm{HCl}$, the rate constant was found to be $5.4 \times 10^{-5} \mathrm{~s}^{-1}$. But in presence of $0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ the rate constant was found to be $6.25 \times 10^{-5} \mathrm{~s}^{-1}$. Thus it may be concluded that :
(a) $\mathrm{H}_{2} \mathrm{SO}_{4}$ furnishes more $\mathrm{H}^{+}$ than $\mathrm{HCl}$
(b) $\mathrm{H}_{2} \mathrm{SO}_{4}$ furnishes less $\mathrm{H}^{+}$ than $\mathrm{HCl}$
(c) both have the same strength
(d) will depend on concentration of ethyl acetato

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Problem 40

For an elementary reaction $2 A+B \longrightarrow A_{2} B$ if the volume of vessel is quickly reduced to half of it's original volume then rate or reaction will
(a) unchange
(b) increase four times
(c) increase eight times
(d) decrease eight times

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Problem 41

In the following reaction $A \rightarrow B+C$, rate constant is $0.001 \mathrm{Ms}^{-1}$. If we start with $1 \mathrm{M}$ of $A$ then conc. of $A$ and $B$ after 10 minutes are respectively :
(a) $0.5 M, 0.5 M$
(b) $0.6 M, 0.4 M$
(c) $0.4 M, 0.6 M$
(d) none of these

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Problem 42

For a reaction $\mathrm{A}-k_{r}=0.6 \mathrm{M} \min ^{-1} \rightarrow 2 B$
starting with $1 \mathrm{M}$ of ${ }^{\prime} A$ ' only, concentration of $B$ (in $M$ ) after 100 sec. and $200 \mathrm{sec}$. is respectively ?
(a) 2 and 4
(b) 1 and 2
(c) 2 and 3
(d) None of thes

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Problem 43

Half-life $\left(t_{1 / 2}\right)$ and completion time $(T)$ of the above reaction $(A \longrightarrow B+C)$ are :
(a) $500 \mathrm{~min}, 750 \mathrm{~min}$
(b) $500 \mathrm{sec}, 750 \mathrm{sec}$
(c) $500 \mathrm{sec}, 1000 \mathrm{sec}$
(d) None of these

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Problem 44

Column Column il
R. Zero order reaction
1. $t_{1 / 2} \propto \frac{1}{[\dot{A}]_{0}}$
Q. First order reaction
2. $t_{100 \%}=[A]_{0} / k$
R. Second order reactions
3. Involves at least two reactants
S. Pseudo unimolecular reaction 4. $[A]=[A]_{0} e^{-k t}$
Code:
(a) $\begin{array}{llll}P & Q & R & S \\ 2 & 1 & 4 & 2 \\ 2 & 4 & 1 & 3 \\ 2 & 1 & 3 & 4 \\ 3 & 2 & 1 & 4\end{array}$
(b)
(c)
(d)

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Problem 45

For the zero order reaction $A \rightarrow B+C ;$ initial concentration of $A$ is $0.1 M$. If $A=0.08 M$ after 10 minutes, then it's half-life and completion time are respectively:
(a) $10 \mathrm{~min} ; 20 \mathrm{~min}$
(b) $2 \times 10^{-3} \min ; 4 \times 10^{-3} \min$
(c) $25 \mathrm{~min}, 50 \mathrm{~min}$
(d) $250 \mathrm{~min}, 500 \mathrm{~min}$

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Problem 46

For an elementary reaction, $X(g) \rightarrow Y(g)+Z(g)$ the half life period is $10 \mathrm{~min}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of original concentration ?
(a) $20 \mathrm{Min}$.
(b) $33 \mathrm{Min}$
(c) $15 \mathrm{Min}$
(d) $25 \mathrm{Min}$

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Problem 47

In the presence of an acid, the initial concentration of cane sugar was reduced from $0.20$ to $0.10$ molar in 5 hours and from $0.2$ to $0.05$ molar in 10 hours. The reaction is of-
(a) Zero order
(b) First order
(c) Second order
(d) Third order

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Problem 48

A first order reaction is $75 \%$ completed in 100 minutes. How long time will it take for it's $87.5 \%$ completion?
(a) $125 \mathrm{~min}$
(b) $150 \mathrm{~min}$
(c) $175 \mathrm{~min}$
(d) $200 \mathrm{~min}$

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Problem 49

The rate constant for a first order reaction whose half life is $480 \mathrm{sec}$.
(a) $1.44 \times 10^{-3} \mathrm{sec}^{-1}$
(b) $1.44 \times \mathrm{sec}^{-1}$
(c) $0.72 \times 10^{-3} \mathrm{sec}^{-3}$
(d) $2.88 \times 10^{-3} \mathrm{sec}^{-3}$

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Problem 50

Rate constant $k=2.303 \mathrm{~min}^{-1}$ for a particular reaction. The initial concentration of reaction is $1 \mathrm{~mol} /$ litre then rate of reaction after 1 minute is :
(a) $2.303 \mathrm{M} \mathrm{min}^{-1}$
(b) $0.2303 \mathrm{M} \mathrm{min}^{-1}$
(c) $0.1 \mathrm{M} \mathrm{min}^{-1}$
(d) none of these

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Problem 51

For the reaction $3 A(g) \stackrel{k}{\longrightarrow} B(g)+C(g), k$ is $10^{-14} \mathrm{~L} / \mathrm{mol} . \mathrm{min}$.
if $[A]=0.5 M$ then the value of $-\frac{d[A]}{d t}$ (in $M \mathrm{~s}^{-1}$ ) is:
(a) $7.5 \times 10^{-5}$
(b) $3 \times 10^{-4}$
(c) $2.5 \times 10^{-5}$
(d) none of these

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Problem 52

$99 \%$ of a first order reaction was completed in 32 minutes when $99.9 \%$ of the reaction wull complete:
(a) $50 \mathrm{~min}$
(b) $46 \mathrm{~min}$
(c) $48 \mathrm{~min}$
(d) $49 \mathrm{~min}$

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Problem 53

Which of the following represents the expression for $\frac{3}{4}$ th life of first order reaction
(a) $\frac{\cdot k}{2.303} \log 4 / 3$
(b) $\frac{2.303}{k} \log 3 / 4$
(c) $\frac{2303}{k} \log 4$
(d) $\frac{2.303}{k} \log 3$

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Problem 54

Consider the following first order competing reactions:
$X \stackrel{k_{1}}{\longrightarrow} A+B \quad$ and $\quad Y \stackrel{k_{2}}{\longrightarrow} C+D$
if $50 \%$ of the reaction of $X$ was completed when $96 \%$ of the reaction of $Y$ was completed, the ratio of their rate constants $\left(k_{2} / k_{1}\right)$ is:
(a) $4.06$
(b) $0.215$
(c) $1.1$
(d) $4.65$

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Problem 55

For the reactions
(i) $A \stackrel{k_{l}}{\longrightarrow} P$
(ii) $B \stackrel{K_{H}}{\longrightarrow} Q$, following observation is made.
4. Time (min). Calculate $\frac{k_{1}}{K_{I I}}$, where $k_{l}$ and $k_{l l}$ and rate constant for the respective reaction.
(a) $2.303$
(b) 1
(c) $0.36$
(d) $0.693$

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Problem 56

The decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ in chloroform was followed by measuring the volume of $\mathrm{O}_{2}$ gas evolved : $2 \mathrm{~N}_{2} \mathrm{O}_{5}\left(\mathrm{CCl}_{4}\right) \stackrel{2}{\longrightarrow} 2 \mathrm{~N}_{2} \mathrm{O}_{4}\left(\mathrm{CCl}_{4}\right)+\mathrm{O}_{2}(g) .$ The maximum volume of $\mathrm{O}_{2}$ gas
obtained was $100 \mathrm{~cm}^{3}$. In 500 minutes, $90 \cdot \mathrm{cm}^{3}$ of $\mathrm{O}_{2}$ were evolved. The first order rate constant (in $\min ^{-1}$ ) for the disappearance of $\mathrm{N}_{2} \mathrm{O}_{5}$ is :
(a) $\frac{2.303}{500}$
(b) $\frac{2.303}{500} \log \frac{100}{90}$
(c) $\frac{2.303}{500} \log \frac{90}{100}$
(d) $\frac{100}{10 \times 500}$

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Problem 57

For a homogeneous gaseous reaction $A \longrightarrow 3 B$, if pressure after time $t$ was $P_{T}$ and after completion of reaction, pressure was $P_{\infty}$ then select correct relation
(a) $k=\frac{1}{t} \ln \left(\frac{P_{\infty}}{3\left(P_{\infty}-P_{t}\right.}\right)$
(b) $k=\frac{1}{t} \cdot \ln \left(\frac{2 P_{\infty}}{3\left(P_{\infty}-P_{T}\right)}\right)$
(c) $k=\frac{1}{t} \ln \left(\frac{3 P_{\infty}}{2 P_{\infty}-P_{t}}\right)$
(d) $k=\frac{1}{t} \ln \left(\frac{2 P_{\infty}}{3\left(P_{\infty}-P_{T}\right)}\right)$

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Problem 58

The half-life of first order decomposition of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ is $2.10 \mathrm{hr}$ at $288 \mathrm{~K}$ temperature $\mathrm{NH}_{4} \mathrm{NO}_{3}(a q) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$, if $6.2 \mathrm{~g}$ of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ is allowed to decompose,
The time required for $\mathrm{NH}_{4} \mathrm{NO}_{3}$ to decompose $90 \%$ and the volume of dry $\mathrm{N}_{2} \mathrm{O}$ produced at this point measured at STP are respectively:
(a) $6.978 \mathrm{hr}, 2.016 \mathrm{~L}$
(b) $0.319 \mathrm{hr}, 2.12 \mathrm{~L}$
(c) $0.319 \mathrm{hr}, 2.016 \mathrm{~L}$
(d) None of these

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Problem 59

For a first order homogeneous gaseous reaction, $A \longrightarrow 2 B+C$ then initial pressure was $P_{i}$ while total pressure after time ' $t$ ' was $P_{t}$. The right expression for the rate constants $k$ in terms of $P_{i}, P_{t}$ and $t$ is :
(a) $k=\frac{2.303}{t} \log \left(\frac{2 P_{i}}{3 P_{i}-P_{t}}\right)$
(b) $k=\frac{2.303}{t} \log \left(\frac{2 P_{i}}{2 P_{t}-P_{i}}\right)$
(c) $k=\frac{2.303}{t} \log \left(\frac{P_{i}}{P_{i}-P_{t}}\right)$
(d) none of these

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Problem 60

The decomposition of azo methane, at certain temperature according to the equation $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}+\mathrm{N}_{2}$ is a first order reaction.
After 40 minutes from the start, the total pressure developed is found to be $350 \mathrm{~mm} \mathrm{Hg}$ in place of initial pressure $200 \mathrm{~mm} \mathrm{Hg}$ of azo methane. The value of rate constant $k$ is :
(a) $2.88 \times 10^{-4} \mathrm{sec}^{-1}$
(b) $1.25 \times 10^{-4} \mathrm{sec}^{-1}$
(c) $5.77 \times 10^{-4} \mathrm{sec}^{-1}$
(d) None of these

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Problem 61

The hydrolysis of sucrose was studied with the help of polarimeter and following data were collected time (min.) $\begin{array}{lll}: 0 & 70 & \infty\end{array}$
observed rotation (degrees) $\begin{array}{lll}: 44 & 16.5 & -11\end{array}$
when the reaction mixture will be optically inactive ? (Given: $\ln 2=0.7, \ln 3=1.1, \ln 5=1.6$ )
(a) 16 min.
(b) $69.47 \mathrm{~min}$.
(c) $160 \mathrm{~min}$.
(d) none of these

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Problem 62

For a particular reaction with initial conc. of the reactants as $a_{1}$ and $a_{2}$, the half-life period are $t_{1}$ and $t_{2}$ respectively. The order of the reaction $(n)$ is given by :
(a) $n=1+\frac{\log \left(t_{2} / t_{1}\right)}{\log \left(a_{2} / a_{1}\right)}$
(b) $n=\frac{\log \left(t_{1} / t_{2}\right)}{\log \left(a_{2} / a_{1}\right)}$
(c) $n=1+\log \frac{\left(t_{1} / t_{2}\right)}{\log \left(a_{2} / a_{1}\right)}$
(d) none of these

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Problem 63

The value of $\frac{t_{0.875}}{t_{0.50}}$ for $n^{t h}$ order reaction is
(a) $2^{(2 n-2)}$
(b) $2^{(2 n-2)-1}$,
(c) $\frac{8^{n-1}-1}{2^{n-1}-1}$
(d) None of these

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Problem 64

$A \longrightarrow B$ first order reaction $A$ is optical active and $B$ is optically inactive, a series of experiment were conducted on a solution of $A$ Time $0 \quad 60 \mathrm{~min} \quad \alpha$
$\begin{array}{llll}\text { optical rotation } & 82^{\circ} & 77^{\circ} & 2^{\circ}\end{array}$
Assume some impurity present calculate the optical rotation after 5 hours. (Given in $\left.1.066=0.064, e^{0.16}=1.17\right)$
(a) 60
(b) 30
(c) 20
(d) 120

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Problem 65

At $300 \mathrm{~K}$ the half-life of a sample of a gaseous compound initially at $1 . \mathrm{atm}$ is $100 \mathrm{sec}$. When the pressure is $0.5$ atm the half-life is $50 \mathrm{sec}$. The order of reaction is :
(a) 0
(b) 1
(c) 2
(d) 3

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Problem 66

concentration of $A$, is equal to :
(a) $2 \times 10^{-3} M \mathrm{~s}^{-1}$
(b) $4 \times 10^{-3} \mathrm{M} \mathrm{s}^{-1}$
(c) $8 \times 10^{-3} M \mathrm{~s}^{-1}$
(d) None of these

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Problem 67

For an endothermic reaction where $\Delta H$ represents the enthalpy of reaction in $\mathrm{kJ} / \mathrm{mol}$, the minimum value for the energy of activation will be :
(a) less than $\Delta H$
(b) more than $\Delta H$
(c) equal to $\Delta H$
(d) zero

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Problem 68

The activation energy of the reaction, $A+B \longrightarrow C+D+38 \mathrm{kcal}$ is $20 \mathrm{kcal}$, What would be the activation energy of the reaction, $C+D \rightarrow A+B$
(a) $20 \mathrm{kcal}$
(b) $-20 \mathrm{kcal}$
(c) $18 \mathrm{kcal}$
(d) 58 kcal

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Problem 69

When the activation energies of the forward and backward reactions are equal, then:
(a) $\Delta E=0, \Delta S=0$
(b) $\Delta E=0 ; \Delta G=0$
(c) $\Delta S=0 ; \Delta G=0$
(d) only $\Delta E=0$

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Problem 70

For an exothermic chemical process occurring in two steps as follows $\begin{array}{ll}\text { (i) } A+B \longrightarrow X \text { (slow) } & \text { (ii) } X \longrightarrow A B \text { (fast) }\end{array}$
The process of reaction can be best describe by:
(a)
(b)
R.C.
(c)
(d)

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Problem 71

Select the correct diagram for an endothermic reaction that proceeds through two steps, with the second step is rate determining :
(b)
(c)
(d)

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Problem 72

$\frac{k_{35^{\circ}}}{k_{34^{\circ}}}>1$, this means that
(a) Rate increases with the rise in temperature
(b) Rate decreases with rise in temperature
(c) rate does not change with rise in temperature
(d) None of the above

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Problem 73

The plot of $\ln k$ versus $1 / T$ is linear with slope of:
(a) $-E_{a} / R$
(b) $E_{a} / R$
(c) $E_{a} / 2.303 R$
(d) $-E_{a} / 2.303 R$

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Problem 74

Rate constant for a chemical reaction takes place at $500 \mathrm{~K}$ is expressed as $k=A . e^{-1000}$ The activation energy of the reaction is:
(a) $100 \mathrm{cal} / \mathrm{mol}$
(b) $1000 \mathrm{kcal} / \mathrm{mol}$
(c) $10^{4} \mathrm{kcal} / \mathrm{mol}$
(d) $10^{6} \mathrm{kcal} / \mathrm{mol}$

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Problem 75

For a complex reaction $A \stackrel{n}{\longrightarrow}$ products
$$
E_{a_{1}}=180 \mathrm{~kJ} / \mathrm{mol} ; \quad E_{a_{2}}=80 \mathrm{~kJ} / \mathrm{mol} ; \quad E_{a_{3}}=50 \mathrm{~kJ} / \mathrm{mol}
$$
Overall rate constant $k$ is related to individual rate constant by the equation $k=\left(\frac{k_{1} \cdot k_{2}}{k_{3}}\right)^{2 / 3}$. Activation energy $(\mathrm{kJ} / \mathrm{mol}$ ) for the overall reaction is :
(a) 100
(b) $43.44$
(c) 150
(d) 140

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Problem 76

For reaction $A \longrightarrow B$, the rate constant $k_{1}=A_{1}\left(e^{-\mathrm{E}_{a} 1^{\prime} \mathrm{H}^{\prime}}\right)$ and for the reaction $X \longrightarrow Y$, the rate constant $k_{2}=A_{2}\left(e^{-E_{a_{2} / R T}}\right) .$ If $A_{1}=10^{9}, A_{2}=10^{10}$ and $E_{a_{1}}=1200 \mathrm{cal} / \mathrm{mol}$, then the
temperature at which $k_{1}=k_{2}$ is: $($ Given $; R=2 \mathrm{cal} / \mathrm{K}-\mathrm{mol})$
(a) $300 \mathrm{~K}$
(b) $300 \times 2.303 \mathrm{~K}$
(c) $\frac{300}{2303} K$
(d) None of these

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Problem 77

The activation energies of the forward and backward reactions in the case of a chemical reaction are $30.5$ and $45.4 \mathrm{~kJ} / \mathrm{mol}$ respectively. The reaction is :
(a) Exothermic
(b) Endothermic
(c) Neither exothermic nor endothermic
(d) Independent of temperature

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Problem 78

A reaction rate constant is given by $: k=1.2 \times 10^{14} e^{\mathrm{RT}} \mathrm{sec}^{-1}$. It means
(a) log k versus $\log T$ will give a straight line with a slope as 25000
(b) $\log k$ versus $\log T$ will give a straight line with a slope as $-25000$
(c) $\log k$ versus $T$ will give a straight line with a slope as $-25000$
(d) $\log k$ versus $1 / T$ will give a straight line

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Problem 79

The temperature coefficient of a reaction is :
(a) The rate constant
(b) The rate constant at a fixed temperature
(c) The ratio of rate constant at two temperature
(d) The ratio of rate constant differing by $10^{\circ} \mathrm{C}$ preferably $k_{308} / k_{298}$

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Problem 80

\text { Which graph shows zero activation energy? }
<smiles>CC</smiles>
(a)
(b)
(c)
(d)

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Problem 81

A homogeneous catalytic reaction takes place through the three alternative plots $A, B$ and $C$ shown in the given figure which one of the following indicates the relative ease with which the reaction can take place ?
(a) $A>B>C$
(b) $C>B>A$
(c) $A>C>B$
(d) $A=B=C$

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Problem 82

A first order reaction is $50 \%$ completed in 20 minutes at $27^{\circ} \mathrm{C}$ and in 5 minutes at $47^{\circ} \mathrm{C}$. The energy of activation of the reaction is :
(a) $43.85 \mathrm{~kJ} / \mathrm{mol}$
(b) $55.14 \mathrm{~kJ} / \mathrm{mol}$
(c) $11.97 \mathrm{~kJ} / \mathrm{mol}$
(d) $6.65 \mathrm{~kJ} / \mathrm{mol}$

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Problem 83

The rate of a reaction gets double when temp changes from $7^{\circ} \mathrm{C}$. By what factor will it change for the temp range $17^{\circ} \mathrm{C}$ to $27^{\circ} \mathrm{C}$.
(a) $1.81$
(b) $1.71$
(c) $1.91$
(d) $1.76$

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Problem 84

Which of the following explains the increase of the reaction rate by catalyst:
(a) Catalyst decreases the rate of backward reaction so that the rate of forward reaction increases
(b) Catalyst provides extra energy to reacting molecules so that they may reduce effective collisions
(c) Catalyst provides an alternative path of lower activation energy to the reactants
(d) Catalyst increases the number of collisions between the reacting molecules.

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Problem 85

Collision theory is satisfactory for:
(a) First order reactions
(b) Zero order reactions
(c) Bimolecular reactions
(d) Any order reactions

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Problem 86

For the first order reaction $A \longrightarrow B+C$, carried out at $27^{\circ} \mathrm{C}$ if $3.8 \times 10^{-16} \%$ of the reactant molecules exists in the activated state, the $E_{a}$ (activation energy) of the reaction is
(a) $12 \mathrm{~kJ} / \mathrm{mole}$
(b) $831.4 \mathrm{~kJ} / \mathrm{mole}$
(c) $100 \mathrm{~kJ} / \mathrm{mole}$
(d) $88.57 \mathrm{~kJ} / \mathrm{mole}$

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Problem 87

A catalyst lowers the activation energy for a certain reaction from $83.314$ to $75 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $500 \mathrm{~K} .$ What will be the rate of reaction as compare to uncatalysed reaction? Assume other things being equal.
(a) Double
(b) 28 times
(c) $7.38$ times
(d) $7.38 \times 10^{\circ}$ times

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Problem 88

A following mechanism has been proposed for a reaction $2 A+B \rightarrow D+E$
$A+B \rightarrow C+D$ (slow)
$A+C \rightarrow E$ (fast)
(a) $r=k[A]^{2}[B]$
(b) $r=k[A][B]$

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Problem 89

A hypothetical reaction $A_{2}+B_{2} \longrightarrow 2 A B$ follows the mechanism as given below $A_{2} \rightleftharpoons A+A$ (fast)
\begin{tabular}{l}
\hline
\end{tabular}
$A+B_{2} \rightarrow A B+B$ (slow)
$A+B \rightarrow A B$ (fast)
The order of the over all reaction is
(a) 2
(b) 1
(c) $\frac{3}{2}$
(d) 0

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Problem 90

Chemical reaction occurs as a result of collisions between reacting molecules. Therefore, the reaction rate is given by
(a) Total number of collisions occurring in a unit volume per second
(b) Fraction of molecules which possess energy less than the threshold energy
(c) Total number of effective collisions which have enough activation energy
(d) none of the above

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Problem 91

Radioactivity is affected by:
(a) temperature
(b) pressure
(c) electric and magnetic field
(d) none of these

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Problem 92

The radiation from naturally occurring radioactive substance as seen atter derlection by a magnetic field in one direction are :
(a) $\alpha$ -rays
(b) $\beta$ -rays
(c) both $\alpha$ and $\beta$ rays
(d) either $\alpha$ or $\beta$ -rays

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Problem 93

In the radioactive decay ${ }_{Z} X^{A} \rightarrow{z+1} Y^{A} \rightarrow{z-1} Z^{A-4} \rightarrow{ }_{z-1} Z^{A-4}$ the sequence of the radiation emitted is :
high energy $\quad$ low energy
(a) $\alpha, \beta, \gamma$
(b) $\gamma, \alpha, \beta$
(c) $\beta, \gamma, \alpha$
(d) $\beta, \alpha, \gamma$

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Problem 94

A radioactive nuclide emitts $\gamma$ -rays due to tne:
(a) emission of an electron from its orbital
(b) nuclear energy transition from a higher state to a lower state
(c) presence of less neutrons than protons
(d) presence of more neutrons than protons

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Problem 95

Consider the following decay ${ }_{z} X^{A} \rightarrow_{z+1} Y^{A}+{ }_{-1} e^{0}, X$ is unstable because :
(a) its nucleus has excess energy
(b) $\frac{n}{p}$ ratio is high
(c) $\frac{n}{p}$ ratio is low
(d) none of these

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Problem 96

Consider the following decay ${ }_{Z} X^{A} \rightarrow{ }_{Z-1} Y^{A}+{ }_{+1} e^{0}\left(\beta^{+}\right) X$ is unstable because :
(a) it's nucleus has excess energy
(b) $\frac{n}{p}$ ratio is high
(c) $\frac{n}{p}$ ratio is low
(d) none of these

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Problem 97

During $\alpha$ -decay :
(a) $\stackrel{n}{-}$ ratio decreases
(b) $\frac{n}{p}$ ratio increases $p$
(c) $\frac{n}{p}$ remains constant
(d) may increase or decrease

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Problem 98

Which of the following processes causes the emission of X-ray?
(a) $\alpha$ -emission
(b) \beta-emission
(c) $\beta^{+}$ (Positron emission)
(d) electron capture

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Problem 99

Which of the following processes result in an increase in the atomic number of a nuclide?
(a) $\alpha$ -emission
(b) electron capture
(c) $\gamma$ -emission
(d) $\beta$ -(Beta)emission

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Problem 100

a........ is produced when a positron and an electron collide.
(a) $X$ -ray
(b) Neutron
(c) $\gamma$ -radiation
(d) Neutrino

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Problem 101

67
$\mathrm{Ho}^{165}$ is stable isotope. ${ }_{67} \mathrm{Ho}^{150}$ is expected to disintegrated by:
(a) $\alpha$ -emission
(b) \beta-emission
(c) positron emission
(d) $\gamma$ -emission

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Problem 102

${ }_{1} \mathrm{H}^{1}$ is a stable isotope. ${ }_{1} \mathrm{H}^{3}$ is expected to disintegrated by :
(a) $\alpha$ -emission
(b) \beta-emission
(c) positron emission
(d) proton emission

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Problem 103

Loss in $\beta$ -particle is equivalent to :
(a) increase of one proton only
(b) decrease of one neutron only
(c) both (a) and (b)
(d) none of these

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Problem 104

Atoms $_{7} X^{n},{ }_{8} Y^{D}$ and ${ }_{9} Z^{17}$ are such that ${ }_{8} Y$ is an isobar of ${ }_{7} X$ and atom ${ }_{9} Z^{17}$ is isotone of ${ }_{8} Y .$ Mass no. of $X$ and no. of neutrons in $Y$ are respectively :
(a) 8,8
(b) 17,7
(c) 9,8
(d) 16,8

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Problem 105

${ }_{90} \mathrm{Th}^{234}$ disintegrate to give ${ }_{82} \mathrm{~Pb}^{206}$ as the final product. Total no. of $\alpha$ and $\beta$ particles emitted out during this process are :
(a) 6
(b) 7
(c) 8
(d) 13

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Problem 106

An isotone of ${ }_{32} \mathrm{Ge}^{76}$ is :
(a) ${ }_{32} \mathrm{Ge}^{77}$
(b) $_{33} \mathrm{As}^{77}$
(c) $_{34} \mathrm{Se}^{77}$
(d) $_{36} \mathrm{Se}^{77}$

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Problem 107

Pair of isobar is :
(a) ${ }_{6} \mathrm{C}^{13},{ }_{7} \mathrm{~N}^{13}$
(b) ${ }_{6} \mathrm{C}^{13},{ }_{7} \mathrm{~N}^{14}$
(c) ${ }_{6} \mathrm{C}^{14} ;{ }_{8} \mathrm{~N}^{15}$
(d) none of these

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Problem 108

Isodiaphers are atoms having:
(a) $n / p$ constant
(b) $p / n$ constant
(c) $(n-p)$ constant
(d) $(n-p)$ different

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Problem 109

The 'Group displacement law' was given by:
(a) Bacqueral
(b) Rutherford
(c) Madam Curie
(d) Soddy and Fajan

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Problem 110

${ }_{3} \mathrm{Li}^{7}+{ }_{1} p^{1} \longrightarrow X$; Identify $X$ if reaction is $(p, \alpha)$ type.
(a) $_{4} \mathrm{Be}^{8}$
1
(b) ${ }_{2} \mathrm{He}^{4}$
(c) ${ }_{0} \gamma^{0}$
(d) none of these
$x$

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Problem 111

Identify reaction type:
${ }_{13} \mathrm{Al}^{27}+{ }_{1} \mathrm{H}^{2} \longrightarrow{ }_{13} \mathrm{Al}^{28}+{ }_{1} \mathrm{H}^{1}$
(a) $(d, p)$
(b) $(p, p)$
(c) $(p, d)$
(d) none of these

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Problem 112

${ }_{13} \mathrm{Al}^{27}+{ }_{1} p^{1} \longrightarrow X+{ }_{0} \gamma^{0} ;$ Identify $X$ if reaction is $(p, \gamma)$ type artificial radioactive reaction.
(a) $_{13} \mathrm{Al}^{28}$
(b) ${ }_{14} \mathrm{Si}^{27}$
(c) ${ }_{14} \mathrm{Si}^{28}$
(d) none of these

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Problem 113

The number of neutrons accompanying in the formation of ${ }_{54} X^{139}$ and ${ }_{38} \mathrm{Sr}^{994}$ from the absorption of slow neutron by ${ }_{92} \mathrm{U}^{235}$ followed by nuclear fission is :
(a) 0
(b) 1
(c) 2
(d) 3 255

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Problem 114

What will be the product of reaction $_{101} \mathrm{Md}^{255}(\alpha, 2 n) ?$
(a) $_{103} \mathrm{Lr}^{256}$
(b) $_{102} \mathrm{No}^{257}$
(c) $_{103} \mathrm{Lr}^{257}$
(d) ${ }_{82} \mathrm{~Pb}^{205}$

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Problem 115

Complete the following nuclear equation by supplying the symbol for the other product of the fission :
$$
{ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \longrightarrow{ }_{38} \mathrm{Sr}^{94}+\ldots \ldots \ldots+2{ }_{0} n^{1}
$$
(a) $_{54} \mathrm{Xe}^{139}$
(b) $_{54} \mathrm{Xe}^{140}$
(c) $_{64} \mathrm{Gd}^{104}$
(d) none of these

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Problem 116

${ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} n \longrightarrow{ }^{139} \mathrm{Ba}+{ }_{36}^{94} \mathrm{Kr}+3_{0}^{1} n+200 \mathrm{MeV}$
Total energy released (in $\mathrm{MeV}$ ) after $5^{\text {th }}$ stage of fission is
(a) 48600
(b) 16200
(c) 24200
(d) None of these

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Problem 117

Proton bombardment of $\mathrm{Th}^{230}$ followed by emission of two alpha particles produce :
(a) $\mathrm{Rn}^{232}$
(b) $\mathrm{Ra}^{233}$
(c) $\mathrm{Fr}^{223}$
(d) $\mathrm{Fr}^{222}$

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Problem 118

${ }_{84} \mathrm{Po}^{210} \longrightarrow{ }_{82} \mathrm{~Pb}^{206}+{ }_{2} \mathrm{He}^{4} .$ In this reaction predict the position of group of Po when $\mathrm{Pb}$ is
in the IV B group :
(a) II B
(b) IV B

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Problem 119

90 Th is a member of III group on losing $\alpha$ -particle forms a new elements belonging to :
(a) I groun
(b) II group
(c) III group
(d) IV group

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Problem 120

Alpha decay of ${ }_{92} \mathrm{U}^{238}$ forms ${ }_{90} \mathrm{Th}^{234} .$ What kind of decay from ${ }_{90}$ Th $\quad$ produces ${ }_{89} \mathrm{Ac}^{234}$ ?
(a) $\alpha$
(b) $\beta$
(c) $\beta^{+}$ (positron)
(d) $\gamma$ -emission

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Problem 121

$\mathrm{Bi}^{214}$ decays to $A$ by $\alpha$ -emission; $A$ then decays to $B$ by beta emission, which decays to $C$ by
83
another beta emission. Element $C$ decays to $D$ by still another beta emission, and $D$ decays by t-emission to a stable isotope $E$. What is an element $E$ ?
(a) $_{81} \mathrm{Tl}^{207}$
(b) ${ }_{80} \mathrm{Hg}^{206}$
(c) ${ }_{79} \mathrm{Au}^{206}$
(d) ${ }_{82} \mathrm{~Pb}^{206}$

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Problem 122

The activity of a radioactive nuclide $\left(X^{10}\right)$ is $6.023$ curie at a certain time $t .$ Ir. 10 disintegration constant is $3.7 \times 10^{4} \mathrm{~s}^{-1}$ the mass of $X$ after $t$ sec is :
(o) 9o.
(h) $1 n^{-13} \sigma$
(c) $10^{-15} \mathrm{~g}$
(d) $10^{-17} \mathrm{~g}$

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Problem 123

Activity of a radioactive substance is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2}\left(t_{2}>t_{1}\right)$, then the ratio of $\frac{A_{2}}{A_{1}}$ is
(a) $e^{\lambda\left(t_{2}+t_{1}\right)}$
(b) $e^{\lambda\left(t_{1}-t_{2}\right)}$
(c) $e^{-\lambda\left(t_{1}+t_{2}\right)}$
(d) $\frac{t_{2}}{t_{1}}$

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Problem 124

The half-life of ${ }_{6} \mathrm{C}^{14}$ is 5730 year. What fraction of it's original $\mathrm{C}^{14}$ would left after 22920 year of storage?
(a) $0.50$
(b) $0.25$
(c) $0.125$
(d) $0.0625$

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Problem 125

A radioactive sample had an initial activity of 56 dpm. After $69.3$ minutes, it was found to have an activity of $28 \mathrm{dpm}$. Find the number of atoms in a sample having an activity of $100 \mathrm{dpm}$.
(a) 693
(b) 100
(c) 1000
(d) 10,000

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Problem 126

A radioactive sample has initial activity of 28 dpm 30 minutes later its activity $14 \mathrm{dpm}$. How many atoms of nuclide were present initially?
(a) 2800
(b) 1217
(c) 528
(d) 2802

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Problem 127

The half-life of $\mathrm{Co}^{60}$ is $5.27$ year $\left(\lambda=2.5 \times 10^{-7} \mathrm{~min}^{-1}\right)$. The activity of $2.09$ of the sample is nearly:
(a) $5 \times 10^{5}$ dpm
(b) $2.5 \times 10^{10} \mathrm{dpm}$
(c) $5 \times 10^{10} \mathrm{dpm}$
(d) $10^{10}$ dpm

Narayan Hari

Numerade Educator

Problem 128

Half-life $\left(t_{1 / 2}\right)$ for a radioactive decay is $6930 \mathrm{sec}$. The time required to fall the rate of decay by $\left(\frac{1}{100}\right)^{\text {th }}$ of it's initial value is :
(a) $69.3 \mathrm{sec}$
(b) $20,000 \mathrm{sec}$
(c) 23030 sèc
(d) none of these

Narayan Hari

Numerade Educator

Problem 129

A sample of radioactive substance is found $90 \%$ of it's initial amount after one day. What $\%$ of the original sample can be found after 3 days?
(a) 81
(b) $72.9$
(c) 25
(d) $65.61$

Narayan Hari

Numerade Educator

Problem 130

If time $t$ is required for a radioactive substance to become one third of it's initial amount, what fraction would be left after $0.5 t ?$
(a) $\frac{1}{2}$
(b) $\frac{1}{\sqrt{3}}$
(c) $\frac{1}{3}$
(d) $\sqrt{\frac{2}{3}}$

Narayan Hari

Numerade Educator

Problem 131

The present activity of the hair of Egyption mummy is $1.75$ dpm. $t_{1 / 2}$ of ${ }_{6} \mathrm{C}^{14}$ is 5770 year and disintegration rate of fresh sample of $\mathrm{C}^{14}$ is $14 \mathrm{dpm}$. Find out age of mummy.
(a) 23080 year
(b) 138480 year
(c) $11998.3$ year
(d) $17313.6$ year

Narayan Hari

Numerade Educator

Problem 132

The amount of ${ }_{6} \mathrm{C}^{14}$ isotope in a piece of wood is found to one fourth $(1 / 4)$ of that present in a fresh piece of wood. Calculate the age of the piece of wood $\left(t_{12}\right.$ of ${ }_{6} \mathrm{C}^{14}=5770$ years)
(a) 7999 year
(b) 11540 year
(c) 16320 year
(d) $23080 \mathrm{v}$

Narayan Hari

Numerade Educator

Problem 133

A radioactive element undergoing decay is left $20 \%$ of it's initial weight after certain period of time $t$, how many such periods should elapse from the start for the $50 \%$ of the element to be left over?
(a) 3
(b) 4
(c) 5
(d) None of these

Narayan Hari

Numerade Educator

Problem 134

In a sample of wood, the reading of a counter is $32 \mathrm{dpm}$ and in a fresh sample of tree it is $122 \mathrm{dpm}$. Due to error counter gives the reading 2 dpm in absence of ${ }^{14} \mathrm{C}$. Half life of ${ }^{14} \mathrm{C}$ is 5770 years. The approximate age (in years) of wood sample is:
(a) $7997.2$
(b) 57570
(c) 11,540
(d) 15140

Narayan Hari

Numerade Educator

Problem 135

A $0.50 \mathrm{~g}$ sample of rock was found to have $25 \times 10^{-6} \mathrm{~mol}$ of ${ }_{19}^{40} \mathrm{~K}\left(t_{1 / 2}=1.3 \times 10^{9} \mathrm{yr}\right)$ and
$7.5 \times 10^{-6} \mathrm{~mol}$ of ${ }_{20}^{40} \mathrm{Ca}$. How old is the rock ?
(a) $6.5 \times 10^{8} \mathrm{yr}$
(b) $1.3 \times 10^{9} \mathrm{yr}$
(c) $2.6 \times 10^{9} \mathrm{yr}$
(d) $5.2 \times 10^{9} \mathrm{yr}$

Narayan Hari

Numerade Educator

Problem 136

Indium- 112 is radioactive and has a very short half-life $\left(t_{1 / 2}=14 \mathrm{~min}\right)$. It's decay constant and, average life are respectively :
(a) $0.0495 \mathrm{~min}^{-1}, 9.7 \mathrm{~min}$
(b) $0.495 \mathrm{~min}^{-1}, 20.2 \mathrm{~min}$
(c) $9.7 \mathrm{~min}^{-1} 20.2 \mathrm{~min}$
(d) $0.0495,20.2 \mathrm{~min}$

Narayan Hari

Numerade Educator

Problem 137

The half-life of radioactive element is 100 minutes. The time interval between the stages to $50 \%$ and $87.5 \%$ decay will be :
(a) $100 \mathrm{~min}$
(b) $50 \mathrm{~min}$
(c) $200 \mathrm{~min}$
(d) $25 \mathrm{~min}$

Narayan Hari

Numerade Educator

Problem 138

The half-life of $\mathrm{Tc}^{99}$ is $6.0 \mathrm{hr}$. The total residual activity in a patient $30 \mathrm{hr}$ after receiving an injection containing $\mathrm{Tc}^{99}$ must be more than $0.01 \mu \mathrm{C}_{i}$. What is the maximum activity (in $\mu \mathrm{C}_{i}$ ) that the sample injected an have?
(a) $0.16$
(b) $0.32$
(c) $0.64$
(d) $0.08$

Narayan Hari

Numerade Educator

Problem 139

A pure radio-chemical preparation was observed to aisinte at the
3.
counts/minutes at $12.35$ PM. At $3.55 \mathrm{PM}$. of the same day, the disintegration rate of the sample was only 535 count/minutes. What is the half-life of the material?
(a) 50
(h) $100 \mathrm{~m}$
(c) $200 \mathrm{~min}$
(d) None of these

Narayan Hari

Numerade Educator

Problem 140

A certain radioactive isotope $z X^{A}\left(t_{1 / 2}=100\right.$ days $)$ decays to $z-2$ If 1 mole of $z_{X}$
kept in sealed container, how much He gas will accumulate at STP in 200 days?
(a) $11.2$ litre
(b) $33.6$ litre
(c) $22.4$ litre
(d) $44.8$ litre

Narayan Hari

Numerade Educator

Problem 141

A radioactive substance decay $25 \%$ in 10 minute. If at start there are $4 \times 10^{20}$ atoms present, after what time will the number of atoms be reduced to $10^{20}$ atoms? (given $\ln 3=1.098$ )
(a) $10.98 \mathrm{~min}$
(b) $21.97 \mathrm{~min}$
(c) $48.19 \mathrm{~min}$
(d) None of these

Narayan Hari

Numerade Educator

Problem 142

The time of decay for a nuclear reaction is given by $t=4 t_{1 / 2}$. The relation between the mean life $(T)$ and time of decay $(t)$ is given by :
(a) $2 T \ln 2$
(b) $4 T \ln 2$
(c) $2 T^{4} \ln 2$
(d) $\frac{1}{T^{2}} \ln 2$

Narayan Hari

Numerade Educator

Problem 143

Two radio isotopes $A$ and $B$ of atomic weight $X$ and $Y$ are mixed in equal amount by weight. After 20 days, their weight ratio is found to be $4: 1$. Isotope. $A$ has a half-life of 1 day. The half-life of isotope $B$ is :
(a) $1.11 \frac{Y}{X}$ day
(b) $0.11 \frac{X}{Y}$ day
(c) $0.6237$ day
(d) $1.11$ day

Narayan Hari

Numerade Educator

Problem 144

Two radioactive nuclides $A$ and $B$ have half-lives $50 \mathrm{~min}$ and $10 \mathrm{~min}$ respectively. A fresh sample contains the nuclide of $B$ to be eight time that of $A$. How much time should elapse so that the number of nuclides of $A$ becomes double of $B$ ?
(a) 30
(b) 40
(c) 50
(d) 100

Narayan Hari

Numerade Educator

Problem 145

A radioactive nuclide is produced at a constant rate of $\alpha$.per second. It's decay constant is $\lambda$. If $N_{0}$ be the no. of nuclei at time $t=0$, then max. no. of nuclei possible are :
(a) $N_{0}$
(b) $\alpha / \lambda$
(c) $N_{0}+\frac{\alpha}{\lambda}$
(d) $\frac{\lambda}{\sigma}+N_{0} s$.

Narayan Hari

Numerade Educator

Problem 146

A radioactive nuclide is produced at a constant rate of $\alpha$.per second. It's decay constant is $\lambda$. If $N_{0}$ be the no. of nuclei at time $t=0$, then max. no. of nuclei possible are :
(a) $N_{0}$
(b) $\alpha / \lambda$
(c) $N_{0}+\frac{\alpha}{\lambda}$
(d) $\frac{\lambda}{\sigma}+N_{0} s$.

Narayan Hari

Numerade Educator

Problem 147

There are two radio nuclei $A$ and $B . A$ is a $\alpha$ -emitter and $B$ is $\beta$ emitter, their disintegration constant are in the ratio of $1: 2$. What should be the number of atoms of two at time $t=0$, so that probability of getting of $\alpha$ and $\beta$ particles are same at time $t=0$ :
(a) $2: 1$
(b) $4: 1$
(c) $1: 2$
(d) $1: 4$

Narayan Hari

Numerade Educator

Problem 148

A radioactive substance (parent) decays to it's daughter element, the age of radioactive substance $(t)$ is related to the daughter $(d) /$ parent $(p)$ ratio by the equation:
(a) $t=\frac{1}{\lambda} \ln \left(1+\frac{p}{d}\right)$
(b) $t=\frac{1}{\lambda} \ln \left(1+\frac{d}{p}\right)$
(c) $t=\frac{1}{\lambda} \ln \left(\frac{d}{p}\right)$
(d) $t=\frac{1}{\lambda} \ln \left(\frac{p}{d}\right)$

Narayan Hari

Numerade Educator

Problem 149

A radioactive substance (parent) decays to it's daughter element, the age of radioactive substance $(t)$ is related to the daughter $(d) /$ parent $(p)$ ratio by the equation:
(a) $t=\frac{1}{\lambda} \ln \left(1+\frac{p}{d}\right)$
(b) $t=\frac{1}{\lambda} \ln \left(1+\frac{d}{p}\right)$
(c) $t=\frac{1}{\lambda} \ln \left(\frac{d}{p}\right)$
(d) $t=\frac{1}{\lambda} \ln \left(\frac{p}{d}\right)$

Narayan Hari

Numerade Educator

Problem 150

${ }_{84} \mathrm{Po}^{218}\left(t_{1 / 2}=183 \mathrm{sec}\right)$ decay to ${ }_{82} \mathrm{~Pb}\left(t_{1 / 2}=16 \mathrm{l} \mathrm{sec}\right)$ by $\alpha$ -emission, while $\mathrm{Pb}^{214}$ is a
3-emitter. In an experiment starting with 1 mole of pure $\mathrm{Po}^{218}$, how much time would be required for the number of nuclei of ${ }_{82} \mathrm{~Pb}^{214}$ to reach maximum?
(a) $147.5$
(b) $247.5$
(c) 182
(d) 304

Narayan Hari

Numerade Educator