# Find the ratio of De-Broglie wavelength of molecules of hydrogen and helium which are at temperatures $\;27^{0} C \;and\; 127^{0} C \;$ respectively

$(a)\;\sqrt{\large\frac{2}{3}}\qquad(b)\;\sqrt{\large\frac{8}{3}}\qquad(c)\;\sqrt{\large\frac{1}{3}}\qquad(d)\;\sqrt{\large\frac{4}{3}}$

Answer : (b) $\;\sqrt{\large\frac{8}{3}}$
Explanation :
de-Broglie wavelength is given by
$\large\frac{\lambda_{H_{2}}}{\lambda_{H_{e}}}=\sqrt{\large\frac{M_{H_{e}}T_{H_{e}}}{M_{H_{2}}T_{H_{2}}}}$
$\sqrt{\large\frac{4}{2}\;\large\frac{(127+273)}{27+273}}=\sqrt{\large\frac{8}{3}}\;.$