Question

The ratio of $d-$Broglie wavelength of molecular of hydrogen and oxygen kept in two vessels separately at ${27}^{o}C$ and ${127}^{o}C$ respectively is:

• A. $\sqrt{\frac{4}{3}}$
• B. $\sqrt{\frac{3}{32}}$
• C. $\frac{8}{\sqrt{3}}$
• D. $\frac{1}{8}$

Answer 1

The correct option is A $\sqrt{\frac{4}{3}}$

We know that,

$\frac{{\lambda H}_2}{{\lambda H}_e}=\frac{\sqrt{M_{H_e}{T}_{H_e}}}{\sqrt{M_{H_2}{T}_{H_2}}}$

Now,

$\frac{{\lambda H}_2}{{\lambda H}_e}=\sqrt{\frac{4(127+273)}{2(27+273)}}$

$\frac{{\lambda H}_2}{{\lambda H}_e}=\sqrt{\frac{1600}{600}}$

$\frac{{\lambda H}_2}{{\lambda H}_e}=\sqrt{\frac{8}{3}}=\sqrt{\frac{4}{3}}$