SATHEE: Atoms And Nuclei Question 379

Atoms And Nuclei Question 379

Question: Two radioactive substances A and B have decay constants $5 λ$ and $λ$ respectively. At t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ${(1 / e)}^{2}$ after a time interval

Options:

A) $4 λ$

B) $2 λ$

C) $1 / 2 λ$

D) $1 / 4 λ$

Show Answer

Answer:

Correct Answer: C

Solution:

$λ_{A} = 5 λ$ and $λ_{B} = λ$

At $t = 0,$

s ${(N_{0})}_{A} = {(N_{0})}_{B}$

Given, $\frac{N_{A}}{N_{B}} = {(\frac{1}{e})}^{2}$

According to radioactive decay, $\frac{N}{N_{0}} = e^{- λ t}$

$∴, \frac{N_{A}}{{(N_{0})}_{A}} = e^{- λ A^{t}}$

and $\frac{N_{B}}{{(N_{0})}_{B}} = e^{- λ, B^{t}}$

From (1) and (2), $\frac{N_{A}}{N_{B}} = e^{- (5 λ - λ) t}$

$\Rightarrow, {(\frac{1}{e})}^{2} = e^{- 4 λ t} = {(\frac{1}{e})}^{4 λ t} \Rightarrow, 4 λ t = 2 ∴, t = \frac{1}{2 λ} .$

Atoms And Nuclei Question 379

Question: Two radioactive substances A and B have decay constants $5 λ$ and $λ$ respectively. At t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ${(1 / e)}^{2}$ after a time interval

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Atoms And Nuclei Question 379

Question: Two radioactive substances A and B have decay constants 5λ and λ respectively. At t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: Two radioactive substances A and B have decay constants $5 λ$ and $λ$ respectively. At t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ${(1 / e)}^{2}$ after a time interval