Question:
The rms speed of oxygen at room temperature is about
\[
500\,\text{m s}^{-1}.
\]
The rms speed of hydrogen at the same temperature is about:
The rms speed of oxygen at room temperature is about
\[
500\,\text{m s}^{-1}.
\]
The rms speed of hydrogen at the same temperature is about:
Show Hint
At the same temperature,
\[
v_{\text{rms}}\propto \frac{1}{\sqrt{M}}.
\]
Lighter gases move faster than heavier gases.
Updated On: Jun 24, 2026
- \(125\,\text{m s}^{-1}\)
- \(2000\,\text{m s}^{-1}\)
- \(8000\,\text{m s}^{-1}\)
- \(500\,\text{m s}^{-1}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Recall the formula for rms speed.
The rms speed of a gas is \[ v_{\text{rms}}=\sqrt{\frac{3RT}{M}} \] Thus, \[ v_{\text{rms}}\propto \frac{1}{\sqrt{M}} \] where \[ M \] is the molar mass of the gas.
Step 2: Write the molar masses.
For oxygen gas: \[ M_{O_2}=32 \] For hydrogen gas: \[ M_{H_2}=2 \]
Step 3: Form the ratio of rms speeds.
\[ \frac{v_{H_2}}{v_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}} \] \[ = \sqrt{\frac{32}{2}} \] \[ = \sqrt{16} \] \[ =4 \]
Step 4: Find the rms speed of hydrogen.
Given, \[ v_{O_2}=500\,\text{m s}^{-1} \] Therefore, \[ v_{H_2}=4\times 500 \] \[ v_{H_2}=2000\,\text{m s}^{-1} \]
Step 5: Final conclusion.
Hence, the rms speed of hydrogen is \[ \boxed{2000\,\text{m s}^{-1}} \]
The rms speed of a gas is \[ v_{\text{rms}}=\sqrt{\frac{3RT}{M}} \] Thus, \[ v_{\text{rms}}\propto \frac{1}{\sqrt{M}} \] where \[ M \] is the molar mass of the gas.
Step 2: Write the molar masses.
For oxygen gas: \[ M_{O_2}=32 \] For hydrogen gas: \[ M_{H_2}=2 \]
Step 3: Form the ratio of rms speeds.
\[ \frac{v_{H_2}}{v_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}} \] \[ = \sqrt{\frac{32}{2}} \] \[ = \sqrt{16} \] \[ =4 \]
Step 4: Find the rms speed of hydrogen.
Given, \[ v_{O_2}=500\,\text{m s}^{-1} \] Therefore, \[ v_{H_2}=4\times 500 \] \[ v_{H_2}=2000\,\text{m s}^{-1} \]
Step 5: Final conclusion.
Hence, the rms speed of hydrogen is \[ \boxed{2000\,\text{m s}^{-1}} \]
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