NEET-XII-Physics
46: The Nucleus
- #27The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old 32P(t1/2 = 14.3 days) source if it was originally purchased for 800 rupees?Ans : Given:
Half-life of 32P source, `` {T}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}``= 14.3 days
Time, t = 30 days = 1 month
Here, the selling rate of a radioactive isotope is decided by its activity.
∴ Selling rate = Activity of the radioactive isotope after 1 month
Initial activity, A0 = 800 disintegration/sec
Disintegration constant `` \left(\lambda \right)`` is given by
`` \lambda =\frac{0.693}{{T}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}`` = `` \frac{0.693}{14.3}{\,\mathrm{\,days\,}}^{-1}``
Activity `` \left(A\right)`` is given by
A = A0e-λt
Here, `` \lambda `` = Disintegration constant
`` \therefore `` Activity of the radioactive isotope after one month (selling rate of the radioactive isotope) `` \left(A\right)`` is given below.
`` A=800\times {e}^{\frac{-0.693}{14.3}\times 30}``
`` =800\times 0.233669``
`` =186.935=\,\mathrm{\,Rs\,}187``
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