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>>First Order Radioactive Decay
>> $The radioactivity of a sample is R1 at a$

Question

The radioactivity of a sample is $R_{1}$ at a time $T_{1}$ and $R_{2}$ at a time $T_{2}$ . If the half-life of the specimen is $T$ , the number of atoms that have disintegrated in the time $(T_{2} - T_{1})$ is proportional to

A

$R_{1} T_{1} - R_{2} T_{2}$

B

$R_{1} - R_{2}$

C

$\frac{( R _{1} - R _{2} )}{T}$

D

$(R_{1} - R_{2}) T$

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is D)

$R_{1} = N_{1} λ$
$R_{2} = N_{2} λ$
$R_{1} - R_{2} = (N_{1} - N_{2}) λ$

Also
$T = \frac{lo g _{e} 2}{λ} \Rightarrow λ = \frac{lo g _{e} 2}{T}$
$R_{1} - R_{2} = (N_{1} - N_{2}) λ$
$R_{1} - R_{2} = (N_{1} - N_{2}) \frac{lo g _{e} 2}{T}$
$\Rightarrow (N_{1} - N_{2}) \propto (R_{1} - R_{2}) T$

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