A radioactive nucleus has 3 times the decay constant as compared to the decay constant of another radioactive nucleus . If initial number of both nuclei are the same, what is the ratio of number of nuclei of to the number of nuclei of , after one half-l

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A radioactive nucleus $n_{2}$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_{1}$ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_{2}$ to the number of nuclei of $n_{1}$ , after one half-life of $n_{1}$ [2025]

1 1/4

2 1/8

3 4

4 8

Ans.
(1)

$λ_{2} = 3 λ$

$λ_{1} = λ$

$N = N_{0} e^{- λ t}$

$N_{1} = N_{0} e^{- λ t}$

$N_{2} = N_{0} e^{- 3 λ t}$

$\frac{N_{2}}{N_{1}} = e^{- 2 λ t}$
$for t = \frac{\ln 2}{λ} \Rightarrow \frac{N_{2}}{N_{1}} = e^{- 2 λ \frac{\ln 2}{λ}} = \frac{1}{4}$

Want Us to Email you About Special Offers & Updates?