A radioactive sample disintegrates via two independent decay processes having half lives T _{1 / 2}^

English

Gujarati

Hindi

13.Nuclei

medium

A radioactive sample disintegrates via two independent decay processes having half lives $T _{1 / 2}^{(1)}$ and $T _{1 / 2}^{(2)}$ respectively. The effective half- life $T _{1 / 2}$ of the nuclei is

A

None of the above

B

$T _{1 / 2}= T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}$

C

$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)} T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}$

D

$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}- T _{1 / 2}^{(2)}}$

(JEE MAIN-2021)

Solution

$\lambda_{ eq }=\lambda_{1}+\lambda_{2}$

$\frac{1}{ T _{1 / 2}}=\frac{1}{ T _{1 / 2}^{(1)}}+\frac{1}{ T _{1 / 2}^{(2)}}$

$T _{1 / 2}=\frac{ T _{1 / 2}^{(1)} T _{1 / 2}^{(2)}}{ T _{1 / 2}^{(1)}+ T _{1 / 2}^{(2)}}$

Standard 12

Physics

Share

Similar Questions

A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is

medium

(AIIMS-2008)

A radio nuclide $A_1$ with decay constant $\lambda_1$ transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$ . If at the initial moment the preparation contained only the radio nuclide $A_1$, then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is :-

normal

In a radioactive substance at $t = 0$, the number of atoms is $8 \times {10^4}$. Its half life period is $3$ years. The number of atoms $1 \times {10^4}$ will remain after interval ………..$years$

medium

A radio-isotope has a half- life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

medium

In Fig. $X$ represents time and $Y$ represent activity of a radioactive sample. Then the activity of sample, varies with time according to the curve

medium