The ratio of d-Brogile wavelength off mlecules of hydrogen and helium gas moving at arms speed in two gas jars kept sparately at temeperature `37^(@)` C and `127^(@)` C respectively is :

Options

A. `(2)/(sqrt3)`
B. 0.085416666666667
C. `(sqrt 3)/(4)`
D. `sqrt(8/(3)`

Answer

D

Explanation

de -Broglie wavlength ` lambda =(h)/(mv)`, where the speed (r.m.s ) of a gas particle at given temperature (T) is given as `(1)/(2)mv^(2)=(3)/(2)kT`, `implies v= sqrt((3KT)/(m))`, where k= Boltzmann's constant and m= mass of the gas particle and T= temperature of the gas in k.`implies mv= sqrt (3mKT)`, `implies lambda=(h)/(mv)=(h)/(sqrt(3mkT))`, `therefore `lambda _(H)/lambda _(He)`=sqrt((m_(He)T_(He))/(m_(H)T_(H)))= sqrt(((4amu)(273+127)^(@)k)/((2amu)(273+27)^(@)k))=sqrt((8)/(3))`