Question

If the relation between time of decay $\left(t\right)$ and half life period $\left(t_{1/2}\right)$ is $(t=4t_{1/2})$; the relation between $t$ and mean life $\left(T\right)$ is:

• A. $\frac{\ln 2}{T^2}$
• B. $2T^4\ln 2$
• C. $4T\ln 2$
• D. $2T\ln 2$

Answer 1

The correct option is C $4T\ln 2$

Relation between $t_{1/2}$ and mean life(T).

$t_{1/2}=\left(ln2\right)T⟶\left(1\right)$

Given, $t=4t_{1/2}⟶\left(2\right)$

Putting value of $t_{1/2}$ in (2) from (1).

$t=4ln2T$