Section 1
Topic 1 : Different Atomic Models that leads to Bohr Model
The difference between the radii of $3^{\text {rd }}$ and $4^{\text {th }}$ orbits of $\mathrm{Li}^{2+}$ is $\Delta \mathrm{R}_{1}$. The difference between the radii of $3^{\text {rd }}$ and $4^{\text {th }}$ orbits of $\mathrm{He}^{+}$is $\Delta \mathrm{R}_{2}$. Ratio $\Delta \mathrm{R}_{1}$ : $\Delta \mathrm{R}_{2}$ is(a) $8: 3$(b) $3: 8$(c) $2: 3$(d) $3: 2$
The region in the electromagnetic spectrum where the Balmer series lines appear is:(a) Visible(b) Microwave(c) Infrared(d) Ultraviolet
The shortest wavelength of $\mathrm{H}$ atom in the Lyman series is $\lambda_{1}$.The longest wavelength in the Balmer series is $\mathrm{He}^{+}$is :(a) $\frac{36 \lambda_{1}}{5}$(b) $\frac{5 \lambda_{1}}{9}$(c) $\frac{9 \lambda_{1}}{5}$(d) $\frac{27 \lambda_{\mathrm{l}}}{5}$
For the Balmer series in the spectrum of $\mathrm{H}$ atom, $\bar{v}=R_{H}\left\{\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\}$, the correct statements among (I) to (IV) are:(I) As wavelength decreases, the lines in the series converge(II) The integer $n_{1}$ is equal to 2(III)The lines of longest wavelength corresponds to $n_{2}=3$(IV) The ionization energy of hydrogen can be calculated from wave number of these lines(a) (I), (III), (IV)(b) (I), (II), (III)(c) (I), (II), (IV)(d) (II), (III), (IV)
The radius of the second Bohr orbit, in terms of the Bohr radius, $a_{0}$, in $\mathrm{Li}^{2+}$ is:(a) $\frac{2 a_{0}}{3}$(b) $\frac{4 a_{0}}{9}$(c) $\frac{4 a_{0}}{3}$(d) $\frac{2 a_{0}}{9}$
Among the following, the energy of $2 s$ orbital is lowest in:(a) $\mathrm{K}$(b) $\mathrm{H}$(c) Li(d) $\mathrm{Na}$
The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9 . The spectral series are :(a) Lyman and Paschen(b) Balmer and Brackett(c) Brackett and Pfund(d) Paschen and Pfund
For any given series of spectral lines of atomic hydrogen, let $\Delta \bar{v}=\bar{v}_{\max }-\bar{v}_{\min }$ be the difference in maximum and minimum frequencies in $\mathrm{cm}^{-1}$. The ratio $\Delta \bar{v}$ $\underset{\text { Lyman }} / \Delta \bar{v}_{\text {Balmer }}$ is :(a) $4: 1$(b) $9: 4$(c) $5: 4$(d) $27: 5$
What is the work function of the metal if the light of wavelength $4000 \AA$ generates photoelectrons of velocity $6 \times 10^{5} \mathrm{~ms}^{-1}$ from it ?(Mass of electron= $9 \times 10^{-31} \mathrm{~kg}$Velocity of light $=3 \times 10^{\circ} \mathrm{ms}^{-1}$Planck's constant $=6.626 \times 10^{-34} \mathrm{~J}_{\mathrm{S}}$Charge of electron $=1.6 \times 10^{-19} \mathrm{JeV}^{-1}$ )(a) $0.9 \mathrm{eV}$(b) $3.1 \mathrm{eV}$(c) $2.1 \mathrm{eV}$(d) $4.0 \mathrm{eV}$
Heat treatment of muscular pain involves radiation of wavelength of about 900 $\mathrm{nm}$. Which spectral line of $\mathrm{H}$-atom is suitable for this purpose?$\left[\mathrm{R}_{\mathrm{H}}=1 \times 10^{5} \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right]$(a) Paschen, $\infty \rightarrow 3$(b) Paschen, $5 \rightarrow 3$(c) Balmer, $\infty \rightarrow 2$(d) Lyman, $\infty \rightarrow 1$
The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. The energy of second excited state of $\mathrm{He}^{+}$ion in $\mathrm{eV}$ is:(a) $-54.4$(b) $-3.4$(c) $-6.04$(d) $-27.2$
Which of the following statements is false?(a) Splitting of spectral lines in electrical field is called Stark effect(b) Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases(c) Photon has momentum as well as wavelength(d) Rydberg constant has unit of energy
Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying $0.5 \mathrm{~V}$ when the radiation of $250 \mathrm{~nm}$ is used. The work function of the metal is :(a) $4 \mathrm{eV}$(b) $5.5 \mathrm{eV}$(c) $4.5 \mathrm{eV}$(d) $5 \mathrm{eV}$
The radius of the second Bohr orbit for hydrogen atom is :(Plank's const. $h=6.6262 \times 10^{-34} \mathrm{Js}$; mass of electron $=9.1091 \times 10^{-31} \mathrm{~kg}$; charge of electron $\mathrm{e}=1.60210 \times 10^{-19} \mathrm{C}$; permittivity of vaccum $\left.\in_{0}=8.854185 \times 10^{-12} \mathrm{~kg}^{-1} \mathrm{~m}^{-3} \mathrm{~A}^{2}\right)$(a) $1.65 \AA$(b) $4.76 \AA$(c) $0.529 \AA$(d) $2.12 \AA$
If the shortest wavelength in Lyman series of hydrogen atom is $\mathrm{A}$, then the longest wavelength in Paschen series of $\mathrm{He}^{+}$is :(a) $\frac{5 \mathrm{~A}}{9}$(b) $\frac{9 \mathrm{~A}}{5}$(c) $\frac{36 \mathrm{~A}}{5}$(d) $\frac{36 \mathrm{~A}}{7}$
A stream of electrons from a heated filaments was passed two charged plates kept at a potential difference $\mathrm{V}$ esu. If ' $\mathrm{e}^{\prime}$ and $m$ are charge and mass of an electron, respectively, then the value of $h / \lambda$ (where $\lambda$ is wavelength associated with electron wave) is given by:(a) $\sqrt{m \mathrm{eV}}$(b) $\sqrt{2 m \mathrm{eV}}$(c) $m \mathrm{eV}$(d) $2 \mathrm{meV}$
Which of the following is the energy of a possible excited state of hydrogen ?(a) $-3.4 \mathrm{eV}$(b) $+6.8 \mathrm{eV}$(c) $+13.6 \mathrm{eV}$(d) $-6.8 \mathrm{eV}$
If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for hydrogen atom, the total energy of the revolving electron will be:(a) $\frac{1}{2} \frac{e^{2}}{r}$(b) $-\frac{e^{2}}{r}$(c) $\frac{m e^{2}}{r}$(d) $-\frac{1}{2} \frac{e^{2}}{r}$
If $\lambda_{0}$ and $\lambda$ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:(a) $\sqrt{\frac{2 h}{m}\left(\lambda_{0}-\lambda\right)}$(b) $\sqrt{\frac{2 h c}{m}\left(\lambda_{0}-\lambda\right)}$(c) $\sqrt{\frac{2 h c}{m}\left(\frac{\lambda_{0}-\lambda}{\lambda \lambda_{0}}\right)}$(d) $\sqrt{\frac{2 h}{m}\left(\frac{1}{\lambda_{0}}-\frac{1}{\lambda}\right)}$
Energy of an electron is given by $\mathrm{E}=-2.178 \times 10^{-18} \mathrm{~J}\left(\frac{Z^{2}}{n^{2}}\right)$. Wavelength of light required to excite an electron in an hydrogen atom from level $n=1$ to $n=2$ will be: $\left(h=6.62 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right.$ and $\left.\mathrm{c}=3.0 \times 10^{8} \mathrm{~ms}^{-1}\right)$(a) $1.214 \times 10^{-7} \mathrm{~m}$(b) $2.816 \times 10^{-7} \mathrm{~m}$(c) $6.500 \times 10^{-7} \mathrm{~m}$(d) $8.500 \times 10^{-7} \mathrm{~m}$
The wave number of the first emission line in the Balmer series of $\mathrm{H}$-Spectrum is :$(\mathrm{R}=$ Rydberg constant $)$ :(a) $\frac{5}{36} R$(b) $\frac{9}{400} R$(c) $\frac{7}{6} R$(d) $\frac{3}{4} R$
The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is $\left[a_{0}\right.$ is Bohr radius] :(a) $\frac{h^{2}}{4 \pi^{2} m a_{0}^{2}}$(b) $\frac{h^{2}}{16 \pi^{2} m a_{0}^{2}}$(c) $\frac{h^{2}}{32 \pi^{2} m a_{0}^{2}}$(d) $\frac{h^{2}}{64 \pi^{2} m a_{0}^{2}}$
Given that the abundances of isotopes ${ }^{54} \mathrm{Fe},{ }^{56} \mathrm{Fe}$ and ${ }^{57} \mathrm{Fe}$ are $5 \%, 90 \%$ and $5 \%$, respectively, the atomic mass of $\mathrm{Fe}$ is(a) $55.85$(b) $55.95$(c) $55.75$(d) $56.05$
The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom?(a) $\mathrm{He}^{+}(n=2)$(b) $\mathrm{Li}^{2+}(n=2)$(c) $\mathrm{Li}^{2+}(n=3)$(d) $\mathrm{Be}^{3+}(n=2)$
Rurtherford's experiment, which established the nuclear model of the atom, used a beam of(a) $\beta$-particles, which impinged on a metal foil and got absorbed(b) $\gamma$-rays, which impinged on a metal foil and ejected electrons(c) helium atoms, which impinged on a metal foil and got scattered(d) helium nuclei, which impinged on a metal foil and got scattered
Which of the following does not characterise X-rays?(a) The radiation can ionise gases(b) It causes $\mathrm{ZnS}$ to fluorescence(c) Deflected by electric and magnetic fields(d) Have wavelengths shorter than ultraviolet rays
The wavelength of a spectral line for an electronic transition is inversely related to(a) the number of electrons undergoing the transition(b) the nuclear charge of the atom(c) the difference in the energy of the energy levels involved in the transition(d) the velocity of the electron undergoing the transition.
The triad of nuclei that is isotonic is(a) ${ }_{6}^{14} \mathrm{C},{ }_{7}^{15} \mathrm{~N},{ }_{9}^{17} \mathrm{~F}$(b) ${ }_{6}^{12} \mathrm{C},{ }^{14}{ }_{7}^{14} \mathrm{~N},{ }_{9}^{19} \mathrm{~F}$(c) ${ }_{6}^{14} \mathrm{C},{ }_{7}^{14} \mathrm{~N},{ }^{17} \mathrm{~F}$(d) ${ }^{14} \mathrm{C},{ }^{14} \mathrm{~N},{ }^{19} \mathrm{~F}$
The ratio of the energy of a photon of $2000 \AA$ wavelength radiation to that of $4000 \AA$ radiation is :(a) $1 / 4$(b) 4(c) $1 / 2$(d) 2
Rutherford's alpha particle scattering experiment eventually led to the conclusion that :(a) mass and energy are related(b) electrons occupy space around the nucleus(c) neutrons are buried deep in the nucleus(d) the point of impact with matter can be precisely determined.
Electromagnetic radiation with maximum wavelength is:(a) ultraviolet(b) radiowave(c) $X$-ray(d) infrared
The radius of an atomic nucleus is of the order of :(a) $10^{-10} \mathrm{~cm}$(b) $10^{-13} \mathrm{~cm}$(c) $10^{-15} \mathrm{~cm}$(d) $10^{-8} \mathrm{~cm}$
Bohr model can explain:(a) the spectrum of hydrogen atom only(b) spectrum of an atom or ion containing one electron only(c) the spectrum of hydrogen molecule(d) the solar spectrum
Which electronic level would allow the hydrogen atom to absorb a photon but not to emit a photon?(a) $3 s$(b) $2 p$(c) $2 s$(d) $1 s$
The increasing order (lowest first) for the values of $e / m$ (charge/mass) for electron $(e)$, proton $(p)$, neutron $(n)$ and alpha particle $(\alpha)$ is :(a) $e, p, n, \alpha$(b) $n, p, e, \alpha$(c) $n, p, \alpha, e$$($ d) $n, \alpha, p-e$
Rutherford's scattering experiment is related to the size of the(a) nucleus(b) atom(c) electron(d) neutron
Rutherford's experiment on scattering of $\alpha$-particles showed for the first time that the atom has(a) electrons(b) protons(c) nucleus(d) neutrons
The number of neutrons in dipositive zinc ion with mass number 70 is(a) 34(b) 36(c) 38(d) 40
The work function $(\varphi)$ of some metals is listed below. The number of metals which will show photoelectric effect when light of $300 \mathrm{~nm}$ wavelength falls on the metal is
Wavelength of high energy transition of H-atoms is $91.2 \mathrm{~nm}$. Calculate the corresponding wavelength of $\mathrm{He}$ atoms.
Calculate the wave number for the shortest wavelength transition in the Balmer series of atomic hydrogen.
According to Bohr's theory, the electronic energy of hydrogen atom in the $n^{\text {ti }}$ Bohr's orbit is given $\operatorname{by} E_{n}=\frac{-21.76 \times 10^{-19}}{n^{2}} \mathrm{~J}$. Calculate the longest wavelength of light that will be needed to remove an electron from the third Bohr orbit of the $\mathrm{He}^{+}$ion.
Calculate the wavelength in Angstrom of the photon that is emitted when an electron in the Bohr orbit, $n=2$ returns to the orbit, $n=1$ in the hydrogen atom. The ionization potential of the ground state hydrogen atom is $2.17 \times 10^{-11}$ erg per atom.
The energy of the electron in the second and the third Bohr's orbits of the hydrogen atom is $-5.42 \times 10^{-12}$ erg and $-2.41 \times 10^{-12}$ erg respectively. Calculate the wavelength of the emitted radiation when the electron drops from the third to the second orbit.
The light radiations with discrete quantities of energy are called $\ldots \ldots \ldots \ldots \ldots .$
Elements of the same mass number but of different atomic numbers are known as __ .
Isotopes of an element differ in the number of $\ldots \ldots \ldots \ldots .$ in their nuclei.
The mass of a hydrogen atom is $\ldots \ldots \ldots . . \mathrm{kg}$.
In a given electric field, $\beta$-particles are deflected more than $\alpha$-particles in spite of $\alpha$-particles having larger charge.
Gamma rays are electromagnetic radiations of wavelengths of $10^{-6} \mathrm{~cm}$ to $10^{-5}$ $\mathrm{cm}$,
The energy of an electron in the first Bohr orbit of $\mathrm{H}$ atom is $-13.6 \mathrm{eV}$. The possible energy value(s) of the excited state(s) for electrons in Bohr orbits of hydrogen is (are)(a) $-3.4 \mathrm{eV}$(b) $-4.2 \mathrm{eV}$(c) $-6.8 \mathrm{eV}$(d) $-1.5 \mathrm{eV}$
The sum of the number of neutrons and proton in the isotope of hydrogen is :(a) 6(b) 2(c) 4(d) 3
When alpha particles are sent through a thin metal foil, most of them go straight through the foil because :(a) alpha particles are much heavier than electrons(b) alpha particles are positively charged(c) most part of the atom is empty space(d) alpha particle move with high velocity
Many elements have non-integral atomic masses because:(a) they have isotopes(b) their isotopes have non-integral masses(c) their isotopes have different masses(d) the constitutents, neutrons, protons and electrons, combine to give fractional masses
An isotone of ${ }_{32}^{76} \mathrm{Ge}$ is:(a) ${ }_{32}^{77} \mathrm{Ge}$(b) ${ }_{33}^{77} \mathrm{As}$(c) ${ }_{34}^{77} \mathrm{Se}$(d) ${ }_{34}^{78} \mathrm{Se}$
Consider the Bohr's model of a one $-$ electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\text {h }}$ orbit of the atom and List-II contains options showing how they depend on $n$List-I List-II(I) Radius of the $n^{\text {h }}$ orbit $\quad$ (P) $\propto n^{-2}$(II) Angular momentum of the electron in the $n^{\text {th }}$ orbit $\quad(\mathrm{Q}) \propto n^{-1}$(III) Kinetic energy of the electron in the $n^{\text {th }}$ orbit $(R) \propto n^{0}$(IV) Potential energy of the electron in the $n^{\text {th }}$ orbit $\quad(\mathrm{S}) \propto n^{1}$(T) $\propto n^{2}$ $(\mathrm{U}) \propto n^{1 / 2}$Which of the following options has the correct ombination considering List-I and List-II?(a) (II), (R)(b) $(\mathrm{II}),(\mathrm{Q})$(c) (I), (P)(d) (I), (T)
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\text {th }}$ orbit of the atom and List-II contains options showing how they depend on $n .$$\begin{array}{ll}\text { List-I } & \text { List-II }\end{array}$I) Radius of the $n^{\text {th }}$ orbit(P) $\propto n^{-2}$II) Angular momentum of the electron in the $n^{\text {th }}$ orbit $\quad(\mathrm{Q}) \propto n^{-1}$III) Kinetic energy of the electron in the $n^{\text {th }}$ orbit $\quad$ (R) $\propto n^{0}$IV) Potential energy of the electron in the $n^{\text {th }}$ orbit $\quad$ (S) $\propto n^{1}$(T) $\propto n^{2}$(U) $\propto n^{1 / 2}$Which of the following options has the correct combination considering List-I and List-II?(a) (III), (S)(b) (IV), (Q)(c) (III), (P)(d) (IV), (U)
Calculate the energy required to excite one litre of hydrogen gas at $1 \mathrm{~atm}$ and $298 \mathrm{~K}$ to the first excited state of atomic hydrogen. The energy for the dissociation of $\mathrm{H}-\mathrm{H}$ bond is $436 \mathrm{~kJ} \mathrm{~mol}^{-1}$.
Consider the hydrogen atom to be a proton embedded in a cavity of radius $a_{0}$ (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in its ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy.
Iodine molecule dissociates into atoms after absorbing light of $4500 \AA$. If one quantum of radiation is absorbed by each molecule, calculate the kinetic energy of iodine atoms. (Bond energy of $\left.\mathrm{I}_{2}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$
Find out the number of waves made by a Bohr electron in one complete revolution in its 3rd orbit.
What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition $n=4$ to $n=2$ of $\mathrm{He}^{+}$spectrum?
Estimate the difference in energy between Ist and 2 nd Bohr orbit for a hydrogen atom. At what minimum atomic number, a transition from $n=2$ to $n=1$ energy level would result in the emission of $X$-rays with $\lambda=3.0 \times 10^{-8} \mathrm{~m}$ ? Which hydrogen atom-like species does this atomic number correspond to?
The electron energy in hydrogen atom is given by $E=\left(-21.7 \times 10^{-12}\right) / n^{2}$ ergs. Calculate the energy required to remove an electron completely from the $n=2$ orbit. What is the longest wavelength (in $\mathrm{cm}$ ) of light that can be used to cause this transition?
Naturally occurring boron consists of two isotopes whose atomic weights are $10.01$ and $11.01 .$ The atomic weight of natural boron is $10.81$. Calculate the percentage of each isotope in natural boron.