The molecules of which of the following gas have highest velocity

The formula for RMS velocity of gas is

${\mathrm{C}}_{\mathrm{rms}}=\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}; \mathrm{Here} \mathrm{R} \mathrm{is} \mathrm{gas} \mathrm{constant}$

T absolute is temperature and M is molar mass of gas.

The gas which has greater value of $\frac{\mathrm{T}}{\mathrm{M}},$it has greater RMS speed.

Case 1: Hydrogen at −50$°$ C

For Hydrogen gas, $\frac{\mathrm{T}}{\mathrm{M}}$Value$=\frac{-50+273}{2}$

$=\frac{223}{2}$

$\therefore {\left(\frac{\mathrm{T}}{\mathrm{M}}\right)}_{{\mathrm{H}}_2}=111.5$

Case 2: For methane  ${\mathrm{CH}}_4 \mathrm{at} 298 \mathrm{K}$

For methane gas, $\frac{\mathrm{T}}{\mathrm{M}} value=\frac{298}{16}=18.6$

$\therefore {\left(\frac{\mathrm{T}}{\mathrm{M}}\right)}_{{\mathrm{CH}}_4}=18.6$

Case 3: For nitrogen at 1000 $°$C :

For nitrogen gas, $=\frac{1000+273}{28}=45.4$

Case 4: For Oxygen at 0 $°$C :

For oxygen gas,  $\frac{\mathrm{T}}{\mathrm{M}} value=\frac{0+273}{32}=8.5$

Among the all cases, hydrogen gas has greater  $\frac{\mathrm{T}}{\mathrm{M}}$so that it has highest RMS velocity..