Question

At a certain temperature, the r.m.s. velocity for $O_2$ is $400m/sec$. at the same temperature, the r.m.s. velocity for $H_2$ molecules will be:

• A. $100m/second$
• B. $25m/second$
• C. $1600m/second$
• D. $6400m/second$

Answer 1

The correct option is C $1600m/second$

Given that,

r. m. s velocity for $O_2=400m/s$

We know that,

$c=\sqrt{\frac{3RT}{m}}$

Now, let at temperature TK r. m. s velocity of $O_2$

$c_{O_2}=\sqrt{\frac{3RT}{M_{O_2}}}.....\left(I\right)$

Now, for $H_2$

$c_{H_2}=\sqrt{\frac{3RT}{m_{H_2}}}....\left(II\right)$

Now, dividing equation (I) by (II)

$\frac{c_{O_2}}{c_{H_2}}=\sqrt{\frac{m_{H_2}}{m_{O_2}}}$

$c_{H_2}=\frac{c_{O_2}}{\sqrt{\frac{m_{H_2}}{m_{O_2}}}}$

$c_{H_2}=\frac{400}{\sqrt{\frac{2}{32}}}$

$c_{H_2}=400\times 4$

$c_{H_2}=1600m/s$

Hence, the r.m.s. velocity for $H_2$ is $1600m/s$