Question

What is the half life of Uranium (atomic number=92, atomic mass=238) if 1µCi of radioactivity requires approximately 7.58×10^21 number of 238^U nuclei?

Answer 1

Number of nuclei is $N=7.58*10^{21}$

Activity of the sample is $R=1 \mu C=3.7×10^{4} decays/s$

The disintegration constant is

$\lambda=\frac{R}{N}=\frac{3.7*10^{4}}{7.58*10^{21}}=4.88*10^{-18} /s$

The half life of the sample is

$T_{1/2}= \frac{ln2}{{4.88*10^{-18}}/s} = 1.42*10^{17} s$