Question

A radioactive substance is being produced at a constant rate of $200$ nuclei/sec. The decay constant of the substance is $1{sec}^{-1}$. After what time will the number of radioactive nuclei become $100$? Initially, there are no nuclei present.

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

Answer 1

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

Since radioactive decay is first order reaction
So, $\lambda =\frac{1}{t}\ln \frac{N_0}{N}$

$⟹t=\ln \left(2\right)sec$