NEET-XII-Physics
46: The Nucleus
- #20The half-life of 199Au is 2.7 days. (a) Find the activity of a sample containing 1.00 µg of 198Au. (b) What will be the activity after 7 days? Take the atomic weight of 198Au to be 198 g mol-1.digAnsr: bAns : Given:
Half-life of 199Au, T1/2= 2.7 days
Disintegration constant, `` \lambda =\frac{0.693}{{T}_{{\displaystyle 1/2}}}`` = `` \frac{0.693}{2.7\times 24\times 60\times 60}=2.97\times {10}^{-6}{\,\mathrm{\,s\,}}^{-1}``
Number of atoms left undecayed, N = `` \frac{1\times {10}^{-6}\times 6.023\times {10}^{23}}{198}``
Now, activity, `` {A}_{0}=\lambda N``
= `` \frac{1\times {10}^{-6}\times 6.023\times {10}^{23}}{198}\times 2.97\times {10}^{-6}``
= 0.244 Ci
(b) After 7 days,
Activity, `` A={A}_{0}{e}^{-\lambda t}``
`` ``
Here, A0 = 0.244 Ci
`` \therefore A=0.244\times {e}^{-2.97\times {10}^{-6}\times 7\times 3600\times 24}``
`` =0.244\times {e}^{17962.56\times {10}^{-4}}``
`` =0.040\,\mathrm{\,Ci\,}``
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