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Chapter 42: Q3Q (page 1301)

At t=0, a sample of radionuclide Ahas the same decay rate as a sample of radionuclide Bhas at. The disintegration constants are位Aand位B, with位A<位B. Will the two samples ever have (simultaneously) the same decay rate? (Hint:Sketch a graph of their activities.)

Short Answer

Expert verified

No, the two samples will never have the same decay rate.

Step by step solution

01

Write the given data

a) Decay rate at of t=0 radionuclide A has same decay rate as radionuclide B at t=30min,R1=R2,

b) Disintegration constants,位A<位B

02

Determine the formulas:  

Write the formula for the disintegration constant:

位=ln2T1/2鈥︹�� (i)

Here, T12is the half-life of the substance.

03

Determine the time of decay

Given that位A<位B

So, from equation (i), the equation becomesT1/2B<T1/2A

It is given that the decay rate of B at t=30 min is the same as the decay rate of A at t=0. Thus, it implies that the decay of radionuclide has already begun and the half-life of B is smaller.

Thus, when the decay of radionuclide A is starting the radionuclide might have already decayed completely.

Hence, there cannot be the same decay rate for the two nuclides.

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