First slide

Radio activity

Question

The activity of a radioactive substance is R at a time t and R/4 at time t = (t + T). Then mean life of the substance is

Moderate

A

T ln4
B

T ln2
C

$\frac{T}{\ln 4}$
D

$\frac{T}{\ln 2}$

Solution

If $R_{0}$ be the initial activity,
$R = R_{0} e^{- λt} and \frac{R}{4} = R_{0} e^{- λ (t + T)}$
$∴ \frac{R}{R / 4} = \frac{e^{- λt}}{e^{- λ (t + T)}} \Rightarrow 4 = e^{λT} \Rightarrow λ = \frac{\ln 4}{T}$
$∴$ Mean life $t_{m} = \frac{1}{λ} = \frac{T}{\ln 4}$

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