Question

Let the most probable velocity of hydrogen molecules at a temp $t^{\circ }\text{C}$ is ${\text{V}}_{\text{o}}$. Suppose all the molecules dissociate into atoms when temp is raised to ${\left(2t+273\right)}^{\circ }\text{C}$ then the new r.m.s velocity is

• A. $\sqrt{2/3}{\text{V}}_{\text{o}}$
• B. $\sqrt{3\left(2+273/t\right)}{\text{V}}_{\text{o}}$
• C. $2\sqrt{3}{\text{V}}_{\text{o}}$
• D. $\sqrt{6}{\text{V}}_{\text{o}}$

Answer 1

Answer: (D)

$\sqrt{6}{\text{V}}_{\text{o}}$

Most probable velocity = $\sqrt{\frac{2RT}{M}}$

at $t^{\circ }C{V}_o=\sqrt{\frac{2R(273+t)}{M_1}}$ ....(i)

After raising temperature

Temperature = $273+2t+273$

$V_o^{\prime }rms=\sqrt{\frac{3R(273+2t+273)}{M_2}}$ ....(ii)

$\frac{V_0^{\prime }rms}{V_0}=\frac{\sqrt{\frac{3R(546+2t)}{1}}}{\sqrt{\frac{2R(273+t)}{2}}}$

$V_0^{\prime }rms=\sqrt{\frac{3(546+2t)}{(273+t)}}{V}_0$

$=\sqrt{3\times 2}$

$V_0=\sqrt{6}{V}_0$