Question

The half-life of1 is 8.04 days. (a) Calculate the decay constant for this isotope. (b) Find the number of 1311 nuclei necessary to of 0.5 uCi produce a sample with an activity

Answer 1

Explanation:

Given that,

$T_{\frac{1}{2}}=8.04\ days$

We need to calculate the decay constant

Using formula of decay constant

$\lambda=\dfrac{0.693}{t_{\frac{1}{2}}}$

$\lambda=\dfrac{0.693}{8.04\times24\times3600}$

$\lambda=9.97\times10^{-7}\ sec^{-1}$

We need to calculate the number of $^{131}I$ nuclei

$N=\dfrac{A\ ci}{\lambda}$

Where,

A= activity

ci = disintegration

$N=\dfrac{0.5\times10^{-6}\times3.7\times10^{10}}{9.97\times10^{-7}}$

$N=1.855\times10^{10}$

Hence, This is the required solution.