The temperature at which the rms speed of atoms in neon gas is equal to the rms speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is: (Atomic mass of neon\(=20.2\) u, molecular mass of hydrogen\(=2\) u)
1. \(2.9\times10^{3}\) K
2. \(2.9\) K
3. \(0.15\times10^{3}\) K
4. \(0.29\times10^{3}\) K

Match Column - I and Column - II and choose the correct match from the given choices.
 

The mean free path for a gas, with molecular diameter \(d\) and number density \(n,\) can be expressed as:
1. $\frac{1}{\sqrt{2}n{\mathrm{\pi d}}^2}$
2. $\frac{1}{\sqrt{2}{n}^2{\mathrm{\pi d}}^2}$
3. $\frac{1}{\sqrt{2}{n}^2{\pi }^2{d}^2}$
4. $\frac{1}{\sqrt{2}n\mathrm{\pi d}}$

A cylinder contains hydrogen gas at a pressure of \(249~\text{kPa}\) and temperature \(27^\circ~\mathrm{C}.\) Its density is: (\(R=8.3~\text{J mol}^{-1}K^{-1}\))
1. \(0.2~\text{kg/m}^{3}\)
2. \(0.1~\text{kg/m}^{3}\)
3. \(0.02~\text{kg/m}^{3}\)
4. \(0.5~\text{kg/m}^{3}\)
$$

The average thermal energy for a mono-atomic gas is:
(\(k_B\) is Boltzmann constant and T absolute temperature)
1. \(\frac{3}{2}k_BT\)
2. \(\frac{5}{2}k_BT\)
3. \(\frac{7}{2}k_BT\)
4. \(\frac{1}{2}k_BT\)

The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:
1.  $l$ $\propto \frac{1}{d^2}$

2.  $l$ $\propto d$

3.  $l$ $\propto$ $d^2$

4.  $l$ $\propto \frac{1}{d}$