The ratio between masses of two particles is `1:2` and ratio between their temperatures is also `1:2`. The ratio between their de-Broglie wavelengths is:

Options

A. `1:2`
B. `2:1`
C. `1:3`
D. `3:1`

Answer

b

Explanation

`E=1/2 mv^(2)=3/2kT`
or `mv=sqrt(3kTm), lambda=h/(mv)`,
So, `lambda_(1)=h/(sqrt(3kT_(1)m_(1))), lambda_(1)=h/(sqrt(3kT_(2)m_(2)))`
`(lambda_(1))/(lambda_(2))=sqrt(((m_(2))/(m_(1)))((T_(2))/(T_(1))))=sqrt((2/1)(2/1))=2`
`(lambda_(1))/(lambda_(2))=2:1`