Question

The activity of a radioactive sample is measured as $9750$ counts ${\left(minute\right)}^{-1}$ at $t=0$ and $975$ counts ${\left(minute\right)}^{-1}$ at $t=5$ minute. The decay constant is nearly

• A. $0.922{min}^{-1}$
• B. $0.691{min}^{-1}$
• C. $0.461{min}^{-1}$
• D. $0.230{min}^{-1}$

Answer 1

The correct option is C $0.461{min}^{-1}$

activity after time$t$ is $N=N_0{e}^{-\lambda t}$

where $N_0$ is activity at $t=0$ putting the above values we get

• decay constant $\lambda =0.461mi{n}^{-1}$
  
• use $\lambda =\left(1/t\right)lo{g}_e\frac{N_0}{N}$ and $lo{g}_{e}10=2.303$