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Q.

At what temperature is the rms speed of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{0} C$ ?

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a

80K

b

3K

c

-73K

d

20 K

answer is A.

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Detailed Solution

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$\frac{V_{H}}{V_{O_{2}}} = \frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{1}}{M_{1}} (\frac{M_{2}}{T_{2}})}$

$V_{1} = V_{2} \Rightarrow \frac{T_{1}}{T_{2}} = \frac{M_{1}}{M_{2}}$

$\Rightarrow \frac{T_{1}}{47 + 273} = \frac{2}{32} = \frac{1}{16}$

$\Rightarrow T_{1} = 20 K$

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At what temperature is the rms speed of gaseous hydrogen molecules equal to that of oxygen molecules at 470C ?