Question

At what temperature is the r.m.s. velocity of a hydrogen
molecule equal to that of an oxygen molecule at 47ºC
(a) 80 K (b) –73 K
(c) 3 K (d) 20 K

Answer 1

Question :-

At what temperature is the r.m.s. velocity of a hydrogen  molecule equal to that of an oxygen molecule at 47ºC  ?

(a) 80 K (b) –73 K

(c) 3 K (d) 20 K

Answer :-

(d) 20 K

Explanation :-

$\sf{V_r_m_s=\sqrt{\dfrac{RT}{M} } }\\\\\sf{\therefore (V_{rms})O_2=(V_{rms})H_2}\\\\\sf{\implies \sqrt{\dfrac{273+47}{32} }=\sqrt{\dfrac{T}{2} }}\\\\\sf{\implies T=20\ K}$

Answer 2

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

$\huge{\underline\bold{OPTION:- D \:\: \huge{\red{\checkmark}}}}$

$\sf{V_r_m_s=\sqrt{\dfrac{RT}{M} } }\\ \\ \sf{\therefore (V_{rms}) O_2=(V_{rms})H_2}\\ \\ \sf{\implies \sqrt{\dfrac{273+47}{32} }=\sqrt{\dfrac{T}{2} }}\\ \\ \sf{\implies T=\dfrac{20}{k} }$