Question

RMS velocity of oxygen molecules at NTP is $0.5 \,km / s$. The RMS velocity for the hydrogen molecule at NTP is

• A. $4\, km / s$
• B. $2 \,km / s$
• C. $3\, km / s$
• D. $1 \,km / s$

Answer 1

Answer: (B)

RMS velocity of molecules at NTP
$V_{ rms }=\sqrt{\frac{3 R T}{M}}$
RMS velocity of oxygen molecules at $NTP$
$\left(v_{1}\right)=\sqrt{\frac{3 R T}{M_{1}}}=0.5 \,km / s$
RMS velocity of hydrogen molecules at NTP
$\left(v_{2}\right) =\sqrt{\frac{3 R T}{M_{2}}} $
$ \Rightarrow \frac{V_{1}}{V_{2}} =\sqrt{\frac{M_{2}}{M_{1}}} $
$\Rightarrow \frac{0.5}{v_{2}} =\sqrt{\frac{2}{32}} $
$\Rightarrow \frac{0.5}{V_{2}} =\frac{1}{4}$
$ v_{2} =2 \,km / s$