What is the de-Broglie wavelength of nitrogen molecule in air at 300K ? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen `=14.0076U`) Plank's constant=`6.63xx10^(-34)Js` , Boltzmann constant `=1.38xx10^(-23)JK^(-1)`

Options

A. `2.75xx10^(-11)m`
B. `2.75xx10^(-12)m`
C. `3.24xx10^(-11)m`
D. `3.24xx10^(-12)m`

Answer

A

Explanation

(a) : Mean kinetic energy of a molecule `(1)/(2)mv_(rms)^(2)=(3)/(2)k_(B)T`
`:.v_(rms)=sqrt((3k_(B)T)/(m))`
`"Here",m=2xx14.0076=28.02u`
As `lamda(h)/(mv_(rms))=(h)/(sqrt(3mk_(B)T))`
`=(6.63xx10^(-34))/(sqrt(3xx(28.2xx1.66xx10^(-27))xx1.38xx10^(-23)xx300))`
`=2.75xx10^(-11)m`