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. \(V_\text{O}>V_\text{H}>V_\text{N}\)

Subtopic:  Types of Velocities |
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Molecular weight of two gases are \(M_1\) 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. \(\sqrt{\frac{M_1-M_2}{M_1+M_2}}\)

Subtopic:  Types of Velocities |
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The root mean square velocity of the molecules of a gas is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is doubled and absolute temperature is halved?

1. 300 m/s 2. 150 m/s
3. 600 m/s 4. 75 m/s
Subtopic:  Types of Velocities |
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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 10Nm-2, rms velocity of its molecules in ms-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2

Subtopic:  Types of Velocities |
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If the ratio of vapour density for hydrogen and oxygen is \(1 \over 16\), then under constant pressure, the ratio of their rms velocities will be:

1. \(4 \over 1\) 2. \(1 \over 4\)
3. \(1 \over 16\) 4. \(16 \over 1\)
Subtopic:  Types of Velocities |
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At which temperature the velocity of \(\mathrm{O_2}\) molecules will be equal to the velocity of \(\mathrm{N_2}\) molecules at \(0^\circ \mathrm{C}?\)

1. \(40^\circ \mathrm{C}\) 2. \(93^\circ \mathrm{C}\)
3. \(39^\circ \mathrm{C}\) 4. Cannot be calculated
Subtopic:  Types of Velocities |
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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. \(4v\)
Subtopic:  Types of Velocities |
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The Earth’s atmosphere contains oxygen and nitrogen. The mass of an oxygen molecule is greater than the mass of a nitrogen molecule. The temperature of the air in a room on a particular day is \(300~\text{K}\). Below are four statements about the motion of the two types of molecules in this room.
A. They have an equal mean square velocity \((\overline{v^2})\).
B. A nitrogen molecule has a greater mean square velocity \((\overline{v^2})\) than an oxygen molecule.
C. A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule.
D. An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule.

Which of the statements is/are correct?
1. Statement A only
2. Statement A and C only
3. Statement B and D only
4. Statement B only
Subtopic:  Types of Velocities |
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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

Subtopic:  Types of Velocities |
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The curve between absolute temperature and \(\mathrm{v}^2_{rms}\) is:

1. 2.
3. 4.
Subtopic:  Types of Velocities |
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