Question

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?

• A. $37\%$
• B. $50\%$
• C. $63\%$
• D. $69\%$

Answer 1

The correct option is C $63\%$

Let number of active nuclei initially be $N_0$ then after time $=meanlife=\frac{1}{\lambda }$

$N=N_o{e}^{-\lambda t}$ gives number of atoms undecayed.

$\therefore$ Number of atoms decayed

$=N_o–N_o{e}^{-\lambda t}$

$=N_o(1-e^{-\lambda t})$

$=N_o(1-e^{-\lambda \left(1/\lambda \right)})$

$=N_o(1-e^{-1})$

$=0.63N_o$

$\therefore$ Percentage decayed $=63$%