Question

A radioactive substance is being consumed at a rate constant of $1s^{-1}$. After what time will the number of radioactive nuclei become $100$. Initially, there were $200$ nuclei present

• A. $1s$
• B. $\frac{1}{ln\left(2\right)}s$
• C. $ln\left(2\right)s$
• D. $2s$

Answer 1

The correct option is C $ln\left(2\right)s$

Given that: $\lambda =1s^{-1}$
We know that half life is given by the relation.
$t_{\frac{1}{2}}=\frac{ln2}{\lambda }=ln2$
Hence the half life period is $=ln2$
Time it takes for $200$ nuclei to decay to $100$ nuclei (50% decay) would be one half life, which is $ln2$ seconds.