(B) The root-mean-square velocity $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.At a given temperature $(T)$,

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(B) The root-mean-square velocity $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.At a given temperature $(T)$,$v_{rms} \propto \frac{1}{\sqrt{M}}$,where $M$ is the molar mass of the gas.The molar masses are: $M_H = 2 \text{ g/mol}$,$M_N = 28 \text{ g/mol}$,and $M_O = 32 \text{ g/mol}$.Since $M_H \frac{1}{\sqrt{M_N}} > \frac{1}{\sqrt{M_O}}$.Therefore,the relationship between the velocities is ${V_H} > {V_N} > {V_O}$.

Class 11 Physics Kinetic Theory of Gases Speed (velocity) of Gas (rms, mean and Most probable speed)

Medium

If ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:

A
${V_N} > {V_O} > {V_H}$
B
${V_H} > {V_N} > {V_O}$
C
${V_O} = {V_N} = {V_H}$
D
${V_O} > {V_H} > {V_N}$

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Class 11

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Kinetic Theory of Gases

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Speed (velocity) of Gas (rms, mean and Most probable speed)

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T \ K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

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At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

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Two containers $A$ and $B$ contain an ideal gas at the same temperature. If the masses of the molecules are $m_A$ and $m_B$ respectively,what is the relationship between their momenta $p_A$ and $p_B$?

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If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

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The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

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If ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:

Similar Questions

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T \ K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

Two containers $A$ and $B$ contain an ideal gas at the same temperature. If the masses of the molecules are $m_A$ and $m_B$ respectively,what is the relationship between their momenta $p_A$ and $p_B$?

If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

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