At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule equal to that of an oxygen molecule at 47 ∘ C?

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At what temperature is the $\mathrm{rms}$ velocity of hydrogen molecule equal to that of an oxygen molecule at $27^{\circ} \mathrm{C} ?$ (a) $10 \mathrm{~K}$ (b) $20 \mathrm{~K}$ (c) $18.75 \mathrm{~K}$ (d) $19.75 \mathrm{~K}$

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At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47∘ CA. 80 KB. 73 KC. 3 KD. 20 K

Text Solution

80 K`-73 K`3 K20 K

Answer : D

Solution : `upsilon_(rms) = sqrt((3RT_(H))/(M_H)) = sqrt((3RT_("OXY"))/(M_("OXY"))` <br> `(T_H)/(M_H) = (T_("OXY"))/(M_("OXY"))` <br> or, `T_(H) = T_("OXY") (M_H)/(M_("OXY")) = (47+273) 2/32 = 320/16` <br> `= 20K`.