Maxwell Distribution

Consider the following statement regarding Maxwell Boltzmann distribution curve.

I. The fraction of molecules with very low or very high speeds is very small.

II. At higher temperatures, the curve near $v_{\mathrm{mp}}$ becomes narrower.

III. The speed possessed by maximum fraction of molecules is known as most probable speed.
Which of the above statement/s is/are incorrect?

In Maxwell-Boltzmann distribution, the fraction of gas molecules having energy between $\mathrm{E}$ and $\mathrm{E}+\mathrm{dE}$ is proportional to

Assertion: Consider a system of gas having N molecules; Instantaneous K.E. of few molecules can be greater than average K.E. of the molecules of the given gas.

Reason: Number of molecules having most probable speed is greater than number of molecules having average speed.

Figure shows a hypothetical speed distribution for particles of a certain gas: $P\left(v\right)=C{v}^2$ for $0<v\le v_0$and $P\left(v\right)=0$ for $v>v_0$. If value of constant $C$ is $x/{v_0}^3$, Find value of $x$. $(N=$Total no of molecules, symbols have their usual meanings)

Assertion: Consider a system of gas having N molecules; Instantaneous K.E. of few molecules can be greater than average K.E. of the molecules of the given gas.

Reason: Number of molecules having most probable speed is greater than number of molecules having average speed.

Which of the following statement is wrong about Maxwell's distribution curve?

What happens when the gas becomes hotter?

How can we find the most probable speed of molecules using maxwell's distribution curve for velocities of molecules of a gas?

Area under maxwell distribution represents the number of number of molecules per unit volume.

If $m$ represents the mass of each molecule of a gas and $T$ its absolute temperature, then the root mean-square velocity of the gaseous molecule is proportional to

Which one of the following series of actions could cause the distribution graph of velocities of gases to change from curve $1$ to curve $2$ as seen below?

$v_{\mathrm{rms}}, v_{\mathrm{av}} \text{and }{v}_{\mathrm{mp}}$ are root-mean-square, average and most probable speeds of molecules of a gas obeying Maxwell's velocity distribution. Which of the following statements is correct?

Explain Maxwell distribution of molecular speeds with necessary graph. 

The expression $n\left(r\right)=n_0{e}^{-\alpha x^4}$ represents the number density of molecules of a gas as a function of distance$r$ from the origin. If it is known that the total number of molecules is proportional to $n_0{\alpha }^{-\mathrm{P}}$, then find the value of $\mathrm{P}$.

Assertion: Maxwell speed distribution graph is symmetric about most probable speed.

Reason: rms speed of ideal gas, depends upon its type (monoatomic, diatomic and polyatomic)

Assertion: In the Maxwellian distribution of speeds in molecules of gases, no. of molecules having speed less than $v_{\mathrm{av}}$ is lesser than number of molecules having speed greater than $v_{\mathrm{av}}$.

Reason: Area under $\frac{dN}{du}$ and $u$ curve is more for molecules having speed greater than $v_{\mathrm{av}}$.

Assertion: The rms velocity of gas molecules having Maxwellian distribution of speeds is greater than their most probable speed.

Reason: The asymmetry of the Maxwellian distribution curve reveals that the number of molecules having speed greater than most probable speed is more than the number of molecules having speed less than the most probable speed.

Which of the following plot is correct about Maxwell's speed distribution law?