SATHEE: Nuclei - Result Question 61

Nuclei - Result Question 61

62. Radioactive material ’ $A$ ’ has decay constant ’ $8 λ$ ’ and material ’ $B$ ’ has decay constant ’ $λ$ ‘. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ‘B’ to that ‘A’ will be $\frac{1}{e}$ ?

[2017]

(a) $\frac{1}{7 λ}$

(b) $\frac{1}{8 λ}$

(d) $\frac{1}{λ}$

Show Answer

Answer:

Correct Answer: 62. (a)

Solution:

(a) Given, $λ_{A} = 8 λ, λ_{B} = λ$

$N_{B} = \frac{N_{A}}{e}$

$\Rightarrow N_{o} e^{- λ_{B} t} = N_{o} \frac{e^{- λ A^{t}}}{e}$

$e^{- λ t} = e^{- 8 λ t} e^{- 1}$

$e^{- λ t} = e^{- 8 λ t - 1}$

Comparing both side powers

$- λ t = - 8 λ t - 1$

$- 1 = 7 λ t$

$t = - \frac{1}{7 λ}$

The best possible answer is $t = \frac{1}{7 λ}$

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Nuclei - Result Question 61

62. Radioactive material ’ A ’ has decay constant ’ 8λ ’ and material ’ B ’ has decay constant ’ λ ‘. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ‘B’ to that ‘A’ will be 1e ?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

62. Radioactive material ’ $A$ ’ has decay constant ’ $8 λ$ ’ and material ’ $B$ ’ has decay constant ’ $λ$ ‘. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ‘B’ to that ‘A’ will be $\frac{1}{e}$ ?