The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which
(i) an electron, and
(ii) a neutron, would have the same de-Broglie wavelength .

Explanation

Givenb Planck's constant `h=6.62xx10^(-34)J`
mass of electron `m_(e)=9.1xx10^(-31)kg`
Mass of electron , `m_(n)1.67xx10^(-27)kg`
Using the relation, `lambda=(h)/(sqrt(2m_(eE)))` we get
`rArr" " lambda^(2)=(h^(2))/(sqrt2m_(e)E')`
`rArrE_(1)=(h^(2))/(2m_(e)lambda^(2))=((6.62xx10^(-34))^(2))/(2xx9.1xx10^(-31)xx(589xx10^(-9))^(2))`
`=6.94xx10^(-25)J`
`=(6.94xx10^(-25))/(1.6xx10^(-19))eV" "( :.1eV=1.6xx10^(-19)J)``=(6.94xx10^(-25))/(1.6xx10^(-19))eV" "( :.1eV=1.6xx10^(-19)J)`
`" " 4.34xx10^(-6)eV`
`E_(2)=KE` of neutron
`rArr" " E_(2)=(h^(2))/(2m_(n)lambda^(2))=((6.62xx10^(-34))^(2))/(2xx1.67xx10^(-27)xx(589xx10^(-9))^(2))`
`" " 3.782xx10^(-28)J`
`" " (3.782xx10^(-28))/(1.6xx10^(-19))eV=2.36xx10^(-9)eV`