Q. No.If \(V_\text{H}\),\(V_\text{N}\) and \(V_\text{O}\) denote the root-mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then:
1. \(V_\text{N}>V_\text{O}>V_\text{H}\)
2. \(V_\text{H}>V_\text{N}>V_\text{O}\)
3. \(V_\text{O}>V_\text{N}>V_\text{H}\)
4. \(V_\text{O}>V_\text{H}>V_\text{N}\)
The molecular weight of two gases is \(M_1\) and \(M_2.\) At any temperature, the ratio of root mean square velocities \(v_1\) and \(v_2\) will be:
1. \(\sqrt{\frac{M_1}{M_2}}\)
2. \(\sqrt{\frac{M_2}{M_1}}\)
3. \(\sqrt{\frac{M_1+M_2}{M_1-M_2}}\)
4. \(\sqrt{\frac{M_1-M_2}{M_1+M_2}}\)
The root mean square velocity of the molecules of a gas is \(300 ~\text{m/s}.\) What will be the root mean square speed of the molecules if the atomic weight is doubled and the absolute temperature is halved?
| 1. | \(300 ~\text{m/s}\) | 2. | \(150 ~\text{m/s}\) |
| 3. | \(600 ~\text{m/s}\) | 4. | \(75 ~\text{m/s}\) |
The molecules of a given mass of gas have rms velocity of 200 ms-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 105 Nm-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 105 Nm-2, rms velocity of its molecules in ms-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3
4.100√2
If the ratio of vapour density for hydrogen and oxygen is \(\frac{1}{16},\) then under constant pressure, the ratio of their RMS velocities will be:
| 1. | \(\frac{4}{1}\) | 2. | \(\frac{1}{4}\) |
| 3. | \(\frac{1}{16}\) | 4. | \(\frac{16}{1}\) |
At which temperature the velocity of \(\mathrm{O_2}\) molecules will be equal to the velocity of \(\mathrm{N_2}\) molecules at \(0^\circ \text{C}?\)
| 1. | \(40^\circ \text{C}\) | 2. | \(93^\circ \text{C}\) |
| 3. | \(39^\circ \text{C}\) | 4. | Cannot be calculated |
The rms speed of the molecules of an enclosed gas is \(v\). What will be the rms speed if the pressure is doubled, keeping the temperature constant?
| 1. | \(v \over 2\) | 2. | \(v\) |
| 3. | \(2v\) | 4. | \(4v\) |
The Earth’s atmosphere contains both oxygen and nitrogen. The mass of an oxygen molecule is greater than that of a nitrogen molecule. On a certain day, the temperature of air in a room is \(300~\text{K}.\)
Consider the following statements regarding the motion of oxygen and nitrogen molecules:
| (A) | Both gases have the same mean square velocity \((\overline{v^2}).\) |
| (B) | Nitrogen molecules have a greater mean square velocity \((\overline{v^2})\) than oxygen molecules. |
| (C) | Nitrogen molecules have a greater mean kinetic energy than oxygen molecules. |
| (D) | Oxygen molecules have a greater mean kinetic energy than nitrogen molecules. |
Choose the correct option from the options given below:
| 1. | (A) only |
| 2. | (A) and (C) only |
| 3. | (B) and (D) only |
| 4. | (B) only |
Uranium has two isotopes of masses \(235 \) and \(238\) units. If both are present in Uranium hexafluoride gas, which would have the larger average speed?
1. \(^{235} \mathrm{U} \mathrm{F}_{6}\)
2. \({}^{238} \mathrm{U} \mathrm{F}_{6}\)
3. Both will have the same average speed.
4. Data insufficient
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