In a radioactive material the activity at time t1 is R1 and at a later time t2 it is R2 . If the decay constant of the material is λ , then

Question

In a radioactive material the activity at time t1 is R1 and at a later time t2 it is R2 . If the decay constant of the material is λ , then (A)  R1 = R2 e-λ(t1-t2)  (B)  R1 = R2 eλ(t1-t2)  (C)  R1 = R2 (t2/t1)  (D)  R1 = R2

Tardigrade Admin · Accepted Answer

The decay rate R of a radioactive material is the number of decays per second.
From radioactive decay law.

- \frac{d N}{d t} \propto N

or

- \frac{d N}{d t} = λ N

Thus,

R = - \frac{d N}{d t}

or

R = λ N

or

R = λ N_{0} e^{- λ t} ... (i)

where

R_{0} = λ N_{0}

is the activity of the radioactive material at time t = 0.
At time

t_{1}, R_{1} = R_{0} e^{- λ t_{1}} ... (ii)

At time

t_{2}, R_{2} = R_{0} e^{- λ t_{2}} ... (iii)

Dividing Eq. (ii) by (iii), we have

\frac{R _{1}}{R _{2}} = \frac{e ^{- λ t_{1}}}{e ^{- λ t_{2}}} = e^{- λ (t_{1} - t_{2})}

or

R_{1} = R_{2} e^{- λ (t_{1} - t_{2})}

Q. In a radioactive material the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$ it is $R_{2}$ . If the decay constant of the material is $λ$ , then

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

$R_{1} = R_{2} e^{λ (t_{1} - t_{2})}$

$R_{1} = R_{2} (t_{2} / t_{1})$

$R_{1} = R_{2}$

Q. In a radioactive material the activity at time t1​ is R1​ and at a later time t2​ it is R2​ . If the decay constant of the material is λ , then

R1​=R2​e−λ(t1​−t2​)

R1​=R2​eλ(t1​−t2​)

R1​=R2​(t2​/t1​)

R1​=R2​

Q. In a radioactive material the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$ it is $R_{2}$ . If the decay constant of the material is $λ$ , then

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

$R_{1} = R_{2} e^{λ (t_{1} - t_{2})}$

$R_{1} = R_{2} (t_{2} / t_{1})$

$R_{1} = R_{2}$