SATHEE: Atoms And Nuclei Question 410

Atoms And Nuclei Question 410

Question: The count rate from a radioactive sample falls from $4.0 \times 10^{6}$ per second to $1 \times 10^{6}$ per second in 20 hour. What will be the count rate, 100 hour after the beginning?

Options:

A) $3.91 \times 10^{3} s e c^{- 1}$

B) $5.81 \times 10^{4} s e c^{- 1}$

C) $6.22 \times 10^{5} s e c^{- 1}$

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

If $A_{0}$ is the initial activity of radioactive sample then activity at any time $A = A_{0} e^{- λ t}$

or $1 \times 10^{6} = 4 \times 10^{6} e^{- λ \times 20}$

or $e^{- 20 λ} = \frac{1}{4}$ The count rate after 100 hour is given by $A^{'} = A_{0} e^{- λ \times 100} = A_{0} e^{- 100 λ} = A_{0} {[e^{- 20 λ}]}^{5}$

$= 4 \times 10^{6} {[\frac{1}{4}]}^{5} = 3.91 \times 10^{3}$ per second

Atoms And Nuclei Question 410

Question: The count rate from a radioactive sample falls from $4.0 \times 10^{6}$ per second to $1 \times 10^{6}$ per second in 20 hour. What will be the count rate, 100 hour after the beginning?

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 410

Question: The count rate from a radioactive sample falls from 4.0×106 per second to 1×106 per second in 20 hour. What will be the count rate, 100 hour after the beginning?

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

Menu

Question: The count rate from a radioactive sample falls from $4.0 \times 10^{6}$ per second to $1 \times 10^{6}$ per second in 20 hour. What will be the count rate, 100 hour after the beginning?