Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1Å and 2 Å . The gases may be considered under identical conditions of temperature, pressure and volume.

This is a short answer type question as classified in NCERT ExemplarMean free path l=1/ 2 d 2 n So n= number of molecules /volumed = diameter of the moleculel ∝ 1 d 2 d1=1Ao, d2=2Aol ∝ 1 d 2 l 1 l 2 = d 2 d 1 2 = 2 1 2 = 4 1 l1:l2=4:1

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Kinetic Theory physics ncert solutions class 11th Physics Class 11th Physics NCERT Exemplar Solutions Class 11th Chapter Thirteen

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1Å and 2 Å . The gases may be considered under identical conditions of temperature, pressure and volume.

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Payal Gupta | Contributor-Level 10

4 months ago

This is a short answer type question as classified in NCERT Exemplar

Mean free path l=1/ $\sqrt[]{2} d^{2} n$

So n= number of molecules /volume

d = diameter of the molecule

l $\propto \frac{1}{d^{2}}$

d₁=1A^o, d₂=2A^o

l $\propto \frac{1}{d^{2}}$

$\frac{l_{1}}{l_{2}} = {(\frac{d_{2}}{d_{1}})}^{2} = {(\frac{2}{1})}^{2} = \frac{4}{1}$

l₁:l₂=4:1

This is a short answer type question as classified in NCERT ExemplarMean free path l=1/ <math> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mi>n</mi> </math> So n= number of molecules /volumed = diameter of the moleculel <math> <mo>∝</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> d1=1Ao, d2=2Aol <math> <mo>∝</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>l</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>l</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </mfrac> </math> l1:l2=4:1

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Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1Å and 2 Å . The gases may be considered under identical conditions of temperature, pressure and volume.

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