question_answer

At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at \[{{47}^{o}}C\]?                                                                                                                        [AIEEE 2002]

A)  80 K                                                                                         

B)  - 73 K

C)  3 K     

D)       20 K

Correct Answer: D

Solution :

[d] The rms velocity of the molecule of a gas of molecular weight M at kelvin temperature T is given by

Let  and  be molecular weights of oxygen and hydrogen and  and  the corresponding kelvin temperatures at which  is same for both gases.

i.e.,

Hence,

Given,