Question

Calculate the time interval between $33$% decay and $66$% decay if half-life of a substance is $20$ minutes:

• A. $40$ minutes
• B. $20$ minutes
• C. $60$ minutes
• D. $13$ minutes

Answer 1

The correct option is B $20$ minutes

We know that,$$N_t=N_0{e}^{-\lambda t}$$ $\Rightarrow ln\left(\frac{0.66}{N_0}\right)=-\lambda t_1$ ...(1)
and $ln\left(\frac{0.33}{N_0}\right)=-\lambda t_2$ ...(2)

Equation (1) $-$ Equation (2):
$\Rightarrow \lambda (t_2-t_1)=ln\left(\frac{0.66}{0.33}\right)=ln2$
$\Rightarrow t_2-t_1=\frac{ln2}{\lambda }=t_{1/2}=20\text{min}$