Given a radioactive nuclide with t1 / 2=1.00 h and a current disintegration rate of 1000 atoms s

Name: Problem 84, Chapter 25: General Chemistry: Principles and Modern Applications
Uploaded: 2020-07-28T20:29:41-08:00
Duration: 2 min 41 s
Channel: Bin Chen
Description: Given a radioactive nuclide with t1 / 2=1.00 h and a current disintegration rate of 1000 atoms s^-1, three hours from now the disintegration rate will be (a) 1000 atoms s^-1 ; (b) 333 atoms s^-1 ; (c) 250 atoms s^-1; (d) 125 atoms s^-1

step 1 Okay, so in this question, they tell us that the half -life is one hour, the time pass is three

Question

Given a radioactive nuclide with $t_{1 / 2}=1.00 \mathrm{h}$ and a current disintegration rate of 1000 atoms $s^{-1}$, three hours from now the disintegration rate will be (a) 1000 atoms $s^{-1} ;$ (b) 333 atoms $s^{-1} ;$ (c) 250 atoms $s^{-1}$; (d) 125 atoms $s^{-1}$

   Given a radioactive nuclide with $t_{1 / 2}=1.00 \mathrm{h}$ and a current disintegration rate of 1000 atoms $s^{-1}$, three hours from now the disintegration rate will be
(a) 1000 atoms $s^{-1} ;$ (b) 333 atoms $s^{-1} ;$ (c) 250 atoms $s^{-1}$;
(d) 125 atoms $s^{-1}$

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci,… 10th Edition

Chapter 25, Problem 84

Instant Answer

Solved by Expert Bin Chen

07/28/2020

Step 1

Plugging in the given half-life of $t_{1 / 2}=1.00 \mathrm{h}$, we have $\lambda=\frac{\ln 2}{1.00 \mathrm{h}}$. Show more…

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Given a radioactive nuclide with $t_{1 / 2}=1.00 \mathrm{h}$ and a current disintegration rate of 1000 atoms $s^{-1}$, three hours from now the disintegration rate will be (a) 1000 atoms $s^{-1} ;$ (b) 333 atoms $s^{-1} ;$ (c) 250 atoms $s^{-1}$; (d) 125 atoms $s^{-1}$

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Key Concepts

Radioactive Decay

This is the process by which unstable atomic nuclei lose energy by emitting radiation. It is a spontaneous process and follows probabilistic laws where the number of decaying nuclei over time can be predicted using the properties of the decay process.

Half-life

Half-life is the time required for half of the original quantity of a radioactive substance to decay. It is a fixed value characteristic of each radioactive nuclide and is central to calculating how the quantity of a substance decreases over time.

Exponential Decay Law

The exponential decay law describes how a quantity decreases over time in a way that the amount remaining is proportional to the exponential function of time. It is expressed mathematically with the formula N(t) = N0 * (1/2)^(t/t1/2), which also applies to the decay rate, showing how the number of disintegrations per second reduces with time.

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