The number density of molecules of a gas depends on their distance r from the origin as n(r)=n_{0}e^{-\alpha r^{4}}. Then the total number of molecules is proportional to:

 

  • Option 1)

    n_{0}\alpha ^{-3/4}

     

  • Option 2)

    \sqrt{n_{0}}\alpha ^{1/2}

  • Option 3)

    n_{0}\alpha ^{1/4}

  • Option 4)

    n_{0}\alpha ^{-3}

 

Answers (1)

 

Maxwell's distribution of molecular speed -

n_{v}dv= 4\pi N\cdot \left ( \frac{m}{2\pi KT} \right )^{3/2}\cdot v^{2}\cdot e\frac{-mv^{2}}{2KT}\cdot dv
 

- wherein

N = total no. of molecules.

m = mass of molecule.

\pi,K,T all have usual meanings.

u = velocity of one particle.

 

 

Total number of molecule = \int ^{\infty }_{o}n(r)dv

=\int ^{\infty }_{o}n_{0}e^{-\alpha r^{4}}4\pi r^{2}dr

Number of molecules is proportional to n_{0}\alpha ^{-3/4}


Option 1)

n_{0}\alpha ^{-3/4}

 

Option 2)

\sqrt{n_{0}}\alpha ^{1/2}

Option 3)

n_{0}\alpha ^{1/4}

Option 4)

n_{0}\alpha ^{-3}

Most Viewed Questions

Preparation Products

JEE Main Rank Booster 2022

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

₹ 13999/- ₹ 6999/-
Buy Now
Knockout JEE Main 2022 (One Month)

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

₹ 13999/- ₹ 6999/-
Buy Now
Knockout JEE Main 2023 (One Month)

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

₹ 13999/- ₹ 6999/-
Buy Now
Knockout JEE Main (Twelve Months Subscription)

AI Powered Self Study Material, Unlimited Mock Tests, Mentorship, Doubt Chat Support, Live Booster Classes and Q&A Discussion.

₹ 23999/- ₹ 14999/-
Buy Now
Knockout JEE Main (Eight Months Subscription)

AI Powered Self Study Material, Unlimited Mock Tests, Mentorship, Doubt Chat Support, Live Booster Classes and Q&A Discussion.

₹ 15999/- ₹ 12499/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions