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# Engineering

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)
S solutionqc

 

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}

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