Question

At what temperature is the r.m.s velocity of hydrogen molecule equal to that of an oxygen molecule at ${47}^{0}C$

• A. $80K$
• B. $-73K$
• C. $3K$
• D. $20K$

Answer 1

Answer: (D)

$20K$

R.m.s velocity of a gas molecule is given as $v_{rms}=\sqrt{\frac{3RT}{M_0}}$

Thus when the r.m.s. velocity of both the gases is same,

$\sqrt{\frac{T_H}{M_H}}=\sqrt{\frac{T_O}{M_O}}$

$⟹T_H=320K\times \frac{2}{32}$

$=20K$