Question

Neutron activation analysis for a sample of a rock revealed the presence of 131 53I, which has a half-life of 8.08 days . Assuming the isotope was freshly separated from its decay products, what is the mass of 131 53I in a sample emitting 1.00 mCi of radiation?

Answer 1

Answer:

The mass of $_{53}^{131}I$ is $8.09\times10^{-9}\ g$.

Explanation:

Given that,

Half life $t_{\frac{1}{2}}=8.08\ days$

Sample emitting radiation = 1.00 mCi = $3.7\times10^{7}\ dps$

We need to calculate the rate constant

Using formula of rate constant

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

$\lambda=\dfrac{0.693}{8.08\times24\times60\times60}$

$\lambda=9.92\times10^{-7}\ s^{-1}$

We need to calculate the numbers of atoms

Using formula of numbers of atoms

$N_{0}=\dfrac{N}{\lambda}$

$N_{0} =\dfrac{3.7\times10^{7}}{9.92\times10^{-7}}$

$N_{0}=3.72\times10^{13}\ atoms$

We need to calculate the mass of $_{53}^{131}I$

Using formula for mass

$m=\dfrac{131\times3.72\times10^{13}}{6.023\times10^{23}}$

$m=8.09\times10^{-9}\ g$

Hence, The mass of $_{53}^{131}I$ is $8.09\times10^{-9}\ g$.