Question

The r.m.s speed of hydrogen gas molecules at a certain temperature is $200{ms}^{-1}$. If the absolute temperature of the gas is doubled and the hydrogen gas dissociates into atomic hydrogen, then the r.m.s speed will become

• A. $200{ms}^{-1}$
• B. $400{ms}^{-1}$
• C. $600{ms}^{-1}$
• D. $800{ms}^{-1}$

Answer 1

Answer: (B)

$400{ms}^{-1}$

$v\propto \sqrt{nT}$ the temperature is double and the hydrogen mlecules are disassociated so $n$ is also doubled. $v_f\propto \sqrt{2n\times 2T}=2\sqrt{nT}\Rightarrow v_f=2v=2\times 200=400m/s$