The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

Question

The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is (A) 600 K (B) 2400 K (C) 1200 K (D) 300 K

Tardigrade Admin · Accepted Answer

√(3RTO/MO)=√(3RTH/MH) or (TO/MO)=(TH/MH) or (TO/32)=(300/2) or TO=16× 300 =4800 K

Q. The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

600 K

2400 K

1200 K

300 K

4800 K

$\frac{3 R T _{O}}{M _{O}} = \frac{3 R T _{H}}{M _{H}}$
or $\frac{T _{O}}{M _{O}} = \frac{T _{H}}{M _{H}}$
or $\frac{T _{O}}{32} = \frac{300}{2}$
or $T_{O} = 16 \times 300$
$= 4800 K$