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In a radioact...

Question

In a radioactive material the activity at time t $_{1}$ is R $_{1}$ and later time at t $_{2}$ , it is R $_{2}$ . If the decay constant of the material is $λ$ , then:

A

R

_{1}

= R

_{2}

e

^{- λ (t_{1} - t_{2})}

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B

R

_{1}

= R

_{2}

e

^{λ (t_{1} - t_{2})}

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C

R

_{1}

= R

_{2} (t_{2} / t_{1})

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D

R

_{1}

= R

_{2}

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Solution

The correct option is D R $_{1}$ = R $_{2}$ e $^{- λ (t_{1} - t_{2})}$
For radioactive decay,

$R (t) = R_{0} e^{- λ t}$
where, $λ \to$ decay constant.

Now,
$R (t_{1}) \to R_{1} R_{1} = R_{0} e^{- λ t_{1}} ⟶$ (1)
$R (t_{2}) \to R_{2} \Rightarrow R_{2} = R_{0} e^{- λ t_{2}} ⟶$ (2)

from equation (2)-
$R_{0} = R_{2} e^{λ t_{2.}}$

Putting value of $R_{0}$ in (1)
$\to R_{1} = R_{2} e^{λ t_{2} - λ t_{1}}$

$\Rightarrow R_{1} = R_{2} e^{- λ (t_{1} - t_{2})}$

Hence, option A is correct.

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