JEE MAIN - Physics (2021 - 27th August Evening Shift - No. 6)
if the rms speed of oxygen molecules at 0$$^\circ$$C is 160 m/s, find the rms speed of hydrogen molecules at 0$$^\circ$$C.
640 m/s
40 m/s
80 m/s
332 m/s
Explanation
$${V_{rms}} = \sqrt {{{3KT} \over M}} $$
$${{{{({V_{rms}})}_{{O_2}}}} \over {{{({V_{rms}})}_{{H_2}}}}} = \sqrt {{{{M_{{H_2}}}} \over {{M_{{O_2}}}}}} = \sqrt {{2 \over {32}}} $$
$${({V_{rms}})_{{H_2}}} = 4 \times {({V_{rms}})_{{O_2}}}$$
$$ = 4 \times 160$$
$$ = 640$$ m/s
$${{{{({V_{rms}})}_{{O_2}}}} \over {{{({V_{rms}})}_{{H_2}}}}} = \sqrt {{{{M_{{H_2}}}} \over {{M_{{O_2}}}}}} = \sqrt {{2 \over {32}}} $$
$${({V_{rms}})_{{H_2}}} = 4 \times {({V_{rms}})_{{O_2}}}$$
$$ = 4 \times 160$$
$$ = 640$$ m/s
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