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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 areλAandλB, withλA<λB. 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,λA<λB

02

Determine the formulas:  

Write the formula for the disintegration constant:

λ=ln2T1/2…… (i)

Here, T12is the half-life of the substance.

03

Determine the time of decay

Given thatλA<λB

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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Most popular questions from this chapter

Suppose the alpha particle in a Rutherford scattering experiment is replaced with a proton of the same initial kinetic energy and also headed directly toward the nucleus of the gold atom. (a) Will the distance from the center of the nucleus at which the proton stops be greater than, less than, or the same as that of the alpha particle? (b) If, instead, we switch the target to a nucleus with a larger value of Z,is the stopping distance of the alpha particle greater than, less than or the same as with the gold target?

Anαparticle (H4enucleus) is to be taken apart in the following steps. Give the energy (work) required for each step: (a) remove a proton, (b) remove a neutron, and (c) separate the remaining proton and neutron. For anαparticle, what are (d) the total binding energy and (e) the binding energy per nucleon? (f) Does either match an answer to (a), (b), or (c)? Here are some atomic masses and neutron mass.

H4e4.00260uH2e2.01410uH3e3.01605uH1e1.00783un1.00867u

After long effort, in 1902 Marie and Pierre Curie succeeded in separating from uranium ore the first substantial quantity of radium, one decigram of pure RaCl2. The radium was the radioactive isotope226Ra, which has a half-life of 1600 y. (a) How many radium nuclei had the Curies isolated? (b) What was the decay rate of their sample, in disintegrations per second?

A radiation detector records 8700 counts in 1.00 min. Assuming that the detector records all decays, what is the activity of the radiation source in (a) Becquerel and (b) curies?

What is the binding energy per nucleon of the americium isotope Am95244? Here are some atomic masses and the neutron mass.

Am95244244.064279uH11.007825un1.008665u
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