Question

Find the fraction of thorium atoms decayed per year if the half-life of thorium $232$ is $1.4\times 10^{10}years$ :

• A. $1\times 10^{-11}$
• B. $4.95\times 10^{-11}$
• C. $0.69\times 10^{-11}$
• D. $7.14\times 10^{-11}$

Answer 1

Answer: (B)

As we know,
given $t_{1/2}=1.4\times 10^{10}years$
$N=N_0{e}^{-\lambda t}$
$\frac{dN}{dt}=-\lambda N\Rightarrow \frac{dN}{N}=-\lambda .dt\dots \dots \dots \left(1\right)$
$\lambda =\frac{ln2}{t_{1/2}}\dots \dots \dots \left(2\right)$
thus, $\frac{dN}{N}=\frac{-ln2.dt}{t_{1/2}}=\frac{-0.693\times 1}{1.4\times 10^{10}}=-4.95\times 10^{-11}$