Photon of wavelength `4xx 10^(7)` strikes on metal surface the work function of the metal being 2.13 eV Calculate (i) The energy of the photon ev (ii) The kinetic energy of the emission and (iii) the velocity of the photoelectron .
`(1 eV = 1.6020 xx 10^(19) J ) `

Explanation

`1 eV = 1.6020 xx 10 ^(19)|` where `lambda = 4 xx 10^(7) m`
`=(2.13 eV xx 1.6020 xx 10^(19)J)/( 1eV ) `
(i) Calculate of energy of photon
`E=- (hc)/( lambda ) = (6.626 xx 10^(34) J s) (3.0 xx 10^(8) ms^(-1))/( 4xx 10^(7) m)`
(ii) Calculation of kinetic energy of emission
Kinetic energy of emission = (photon energy work function W )
`=(4.9695 xx 10^(19) - 3.4123 xx 10^(19)J`
(iii) Calculation of velocity of the photoelectron kinetic energy `1.56 xx 10^(19) J`
Kinetic energy `=(1)/(2) mV^(2)`
`v^(2) = (2xx "kinetic energy ")/( m )`
`=sqrt((2xx 1.56 xx 10^(19))/(9.1 xx 10^(31) kg ))`
`= sqrt (0.3429 xx 10^(12) kg^(-1))`
`=0.5855 xx 10^(6) ms^(-1) `
`5.855 xx 10^(5) ms^(-1)`