Question

The decay constant of radioactive sample is $\lambda$. The half-life and mean-life of the sample are, respectively, given by

• A. $1/\lambda$ and $\left(ln2\right)/\lambda$
• B. $\left(ln2\right)/\lambda$ and $1/\lambda$
• C. $\lambda /\left(ln2\right)$ and $1/\lambda$
• D. $\lambda \left(ln2\right)$ and $1/\lambda$

Answer 1

Answer: (B)

We know that, $N=N_0{e}^{-\lambda t}$
$e^{\lambda t}=\frac{N_0}{N}\Rightarrow \lambda t=ln\left(\frac{N_0}{N}\right)$