Paragraph According to Maxwell distribution law, the probability distribution function is given as below: F(v)=4 π( M 2 π R T )^ 3 / 2 v^2 ^ -M v^2 / 2 R ~T M-molar mass of gas, v-speed, R-gas constant, T-Absolute

Correct answer: D. v_ ms =∫_0^ ∞ v f(v) d v v_ avg =∫_0^ ∞ vf(v) d vv_ m p =(d f(v))/(d v)=0v_ rms ^2=∫_0^ ∞ v^2 f(v) d v

JEE Advanced

JEE Advanced · Chemistry · States of Matter

Paragraph According to Maxwell distribution law, the probability...

Paragraph According to Maxwell distribution law, the probability distribution function is given as below:

\mathbf{F}(\mathrm{v})=4 \pi\left(\frac{\mathrm{M}}{2 \pi \mathbf{R T}}\right)^{3 / 2} \mathrm{v}^2 \mathrme^{-M \mathrm{v}^2 / 2 R \mathrm{~T}}

M-molar mass of gas, v-speed, R-gas constant, T-Absolute temperature Fraction of molecule in the range of

v_1

v_2=\int_{v_1}^{v_2} f(v) d v

Question Average speed (

\mathrm{V}_{\text {avg }}

) most probable speed (

\mathrm{v}_{\mathrm{mp}}

) and root mean square (

\mathrm{v}_{\mathrm{ms}}

) speeds can be derived from Maxwell distribution. Choose the incorrect option regarding molecular speeds

D. $v_{\mathrm{ms}}=\int_0^{\infty} v \sqrt{f(v)} d v$

\mathbf{v}_{\mathrm{avg}}=\int_0^{\infty} \mathrm{vf}(\mathrm{v}) \mathbf{d v}v_{m p}=\frac{d f(v)}{d v}=0\mathbf{v}_{\mathrm{rms}}^2=\int_0^{\infty} \mathbf{v}^2 \mathbf{f}(\mathbf{v}) \mathbf{d v}