Question:
A flask of volume 0.1 m\(^3\) contains He (monatomic) and O\(_2\) (diatomic) gases in the ratio 4:1. The flask is maintained at a temperature 27 °C. The ratio of the rms speeds of the He-atoms and O\(_2\)-molecules is:
(Atomic mass of He = 4 amu, and O\(_2\) = 32 amu)
A flask of volume 0.1 m\(^3\) contains He (monatomic) and O\(_2\) (diatomic) gases in the ratio 4:1. The flask is maintained at a temperature 27 °C. The ratio of the rms speeds of the He-atoms and O\(_2\)-molecules is:
(Atomic mass of He = 4 amu, and O\(_2\) = 32 amu)
(Atomic mass of He = 4 amu, and O\(_2\) = 32 amu)
Show Hint
RMS speed depends on particle mass: \(v_\text{rms} \propto 1/\sqrt{m}\). For gases at the same temperature, lighter particles move faster. Multiply by factor if multiple types of particles exist in mixture.
Updated On: Jun 19, 2026
- 2 : 1
- 4 : 1
- \(2 \sqrt{2} : 1\)
- \(\sqrt{2} : 1\)
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The Correct Option is C
Solution and Explanation
Step 1: Recall rms speed formula.
The rms speed of a gas particle is: \[ v_\text{rms} = \sqrt{\frac{3 k_B T}{m}} \] where \(k_B\) is Boltzmann’s constant, \(T\) is temperature in Kelvin, and \(m\) is mass of a single particle.
Step 2: Consider relative numbers.
The flask contains He:O\(_2\) in ratio 4:1 by number of particles. Mass of He atom \(m_\text{He} = 4~\text{amu}\), mass of O\(_2\) molecule \(m_\text{O2} = 32~\text{amu}\).
Step 3: Compute ratio of rms speeds.
\[ \frac{v_\text{rms,He}}{v_\text{rms,O2}} = \sqrt{\frac{m_\text{O2}}{m_\text{He}}} = \sqrt{\frac{32}{4}} = \sqrt{8} = 2 \sqrt{2} \]
Step 4: Conclusion.
Hence, the ratio of rms speeds of He-atoms to O\(_2\)-molecules is \(2 \sqrt{2} : 1\).
The rms speed of a gas particle is: \[ v_\text{rms} = \sqrt{\frac{3 k_B T}{m}} \] where \(k_B\) is Boltzmann’s constant, \(T\) is temperature in Kelvin, and \(m\) is mass of a single particle.
Step 2: Consider relative numbers.
The flask contains He:O\(_2\) in ratio 4:1 by number of particles. Mass of He atom \(m_\text{He} = 4~\text{amu}\), mass of O\(_2\) molecule \(m_\text{O2} = 32~\text{amu}\).
Step 3: Compute ratio of rms speeds.
\[ \frac{v_\text{rms,He}}{v_\text{rms,O2}} = \sqrt{\frac{m_\text{O2}}{m_\text{He}}} = \sqrt{\frac{32}{4}} = \sqrt{8} = 2 \sqrt{2} \]
Step 4: Conclusion.
Hence, the ratio of rms speeds of He-atoms to O\(_2\)-molecules is \(2 \sqrt{2} : 1\).
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