What is the de Broglie wavelength of a nitrogen molecule in air at 300 K ? Assume that the molecule is moving with the root-mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)

Explanation

`T =300K " " lambda=?`
`m=14.0076u=14.0076xx1.6xx10^(-27)kg `
`K_("max")=(3)/(2)KT=(3)/(2)xx1.38xx10^(-23)xx300=6.21xx10^(-21)J`
`p=sqrt(2mK_("max"))=sqrt(2xx14.0076xx1.6xx10^(-27)xx6.21xx10^(-21))=1.7xx10^(-23)kg ms^(-1)`
`lambda=(h)/(p)=(6.6xx10^(-34))/(1.7xx10^(-23))=3.9xx10^(-11)m`