A radioactive nucleus A with a half life T, decays into a nucleus B.  At t=0, there is no nucleus B.  At sometime t, the ratio of the number of B to that of A is 0.3.  Then, t is given by :

  • Option 1)

    t= \frac{T}{2}\: \: \frac{\log 2}{\log 1.3}

  • Option 2)

    t= T\frac{\log 1.3}{\log 2}

  • Option 3)

    t= T\log \left ( 1.3 \right )

  • Option 4)

    t= \frac{T}{\log 1.3}

 

Answers (1)

As we learnt in

Number of nuclei after disintegration -

N=N_{0}e^{-\lambda t} or A=A_{0}e^{-\lambda t}

- wherein

Number of nucleor activity at a time is exponentional function

 

 Number of nucleus of A at any time t is 

N_{A}=N_{0}.E^{-\lambda t}

NB= Number of nucleus of A that decayed tinto B

=N_{0}\left(1-e^{-\lambda t} \right )

\frac{N_{B}}{N_}=\frac{1-e^{-\lambda t}}{e^{-\lambda t}}=0.3

\therefore\ \; 1-e^{-\lambda t}=0.3e^{-\lambda t}\ or\; 1.3e^{-\lambda t}=1

1-e^{-\lambda t}=\frac{1}{1.3}

Taking log

\lambda t=log_{e}1.3

t.\left(\frac{log_{e}\ {2}}{T} \right )=log_{e}\ 1.3

t=T\frac{log_{e}1.3}{log_{e}2}

Correct answer is 2


Option 1)

t= \frac{T}{2}\: \: \frac{\log 2}{\log 1.3}

This is an incorrect option.

Option 2)

t= T\frac{\log 1.3}{\log 2}

This is the correct option.

Option 3)

t= T\log \left ( 1.3 \right )

This is an incorrect option.

Option 4)

t= \frac{T}{\log 1.3}

This is an incorrect option.

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions