A photon of wavelength ` 4xx 10^(-7)` m strikes on metal surface. The work funcation of the metal being 2.13eV. Calculate (i) the energy of the photon (eV) . (ii) the kinetic energy of the emission, and (ii) the velcoity of the photoelectron `(1 eV= 1.6020 xx 10^(-19) J )`

Explanation

According to Einstein.s photoelectric equation
`hv=W+1/2 mv^2`
In the present case,
`v=c/lambda=(3 xx 10^(8))/(4 xx 10^(-7))=7.5 xx 10^(14) s^(-1)`
`W=2.13eV=2.13 xx 1.6020 xx 10^(-19)J=3.41 xx 10^(-19)J`
m=mass of electron `=9.109 xx 10^(-31)kg`
(i) Energy of photon =hv
`=6.626 xx 10^(-34) xx 7.5 xx 10^(14)`
`=4.97 xx 10^(-19)J`
`=(4.97 xx 10^(-19))/(1.6020 xx 10^(-19))=3.102eV`
(ii) Kinetic energy of emission `=1/2 mv^2=hv-W`
`=4.97 xx 10^(-19)-3.41 xx 10^(-19)`
`=1.56 xx 10^(-19)J=0.97eV`
(ii) `1/2 mv^2=1.56 xx 10^(-19)`
`v=((2 xx 1.56 xx 10^(-19))/(m))^(1/2)`
`=(2 xx 1.56 xx 10^(-19))/(9.109 xx 10^(-31))^(1/2)`
`=5.85 xx 10^(5) ms^(-1)`