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Question: The ratio between the rms velocity of H<sub>2</sub> at 50 K and that of O<sub>2</sub> at 800 K is...

The ratio between the rms velocity of H2 at 50 K and that of O2 at 800 K is

A

4

B

2

C

1

D

¼

Answer

1

Explanation

Solution

Vrms (H2 at 50 K) = 3R×502×10−3\sqrt{\frac{3R \times 50}{2 \times 10^{- 3}}}

Vrms (O2 at 800K) = 3R×80032×10−3\sqrt{\frac{3R \times 800}{32 \times 10^{- 3}}}

Vrms(H2)Vrms(O2)=3R×502×10−33R×80032×10−3=25×10325×103=1\frac{V_{rms}(H_{2})}{V_{rms}(O_{2})} = \frac{\sqrt{\frac{3R \times 50}{2 \times 10^{- 3}}}}{\sqrt{\frac{3R \times 800}{32 \times 10^{- 3}}}} = \frac{\sqrt{25 \times 10^{3}}}{\sqrt{25 \times 10^{3}}} = 1