The temperature at which RMS velocity of SO2 molecules is half that of He molecu

Question

The temperature at which RMS velocity of

S O_{2}

molecules is half that of He molecules at 300 K is

Options:

A . 150 K

B . 600 K

C . 900 K

D . 1200 K

Answer: Option D
:
D

\frac{U_{S O_{2}}}{U_{H} e} = \frac{1}{2} = \sqrt{\frac{M_{H e}}{M_{S O_{2}}} \frac{T_{S O_{2}}}{T_{H e}}} = \sqrt{\frac{4}{64} \frac{T_{S O_{2}}}{300}}

= \frac{4}{64} \frac{T_{S O_{2}}}{300} = \frac{1}{4}; T_{S O_{2}} = 1200^{\circ} K

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