Question

Sample containing ${}_{88}^{234}Ra$, which decays by $\alpha -$particle emission, is observed to disintegrate at the following rate expressed as counts per minute (cpm). Calculate half-life of this nuclide. $t=0,1000cpm;t=1h,992cpm;t=10h,924cpm;t=100h,452cpm;t=250h,138cpm$.

Answer 1

$t=0,Cpm=1000$

$t=1hr,Cpm=992$

$At=A_0{\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$

$992=1000{\left(\frac{1}{2}\right)}^{\frac{1hr}{t_{1/2}}}\Rightarrow ={\left(\frac{1}{2}\right)}^{\frac{1hr}{t_{1/2}}}$

$\log \left(0.992\right)=\frac{-1hr}{t_{1/2}}\log 2\Rightarrow -3.488\times {10}^{-3}=\frac{-1hr}{t_{1/2}}\times 0.3010$

$t_{1/2}=\frac{0.03010}{3.488\times {10}^{-3}}=86.3hr\therefore t_{1/2}=\frac{86.3hr}{24}=3.59$ days.