Question

Find the ratio of $deBroglie$ wavelength of molecules of hydrogen and helium which are at temperature ${27}^{o}C$ and ${127}^{o}C$ respectiovely.

• A. $\sqrt{\frac{5}{3}}$
• B. $\sqrt{\frac{8}{3}}$
• C. $\sqrt{\frac{3}{5}}$
• D. $\sqrt{\frac{3}{8}}$

Answer 1

The correct option is B $\sqrt{\frac{8}{3}}$

De-Broglie wavelength is given by

We know that,

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

$=\sqrt{\frac{4}{2}\frac{(127+223)}{27+273}}=\sqrt{\frac{8}{3}}$