Calculate the velocity of electron ejected from a platium surface when radiation of `200 `nm falls on it .The work function of platinum is `5 eV(1 eV = 1.6 xx 10^(-19) J)`

Explanation

Wavelength of radiation `(lambda) = 200 nm = 200 xx 10^(-6)m)`
`E_("total")=(hc)/lambda=(6.63xx10^(-34)Jsxx3xx10^(8)ms^(-1))/(250xx10^(-9)m)`
`=7.956xx10^(-19)J`
Work function `(W) = 5 eV =5 xx 1.6 xx 10^(-19)J = 8.0 xx 10^(-19)J`
Energy of photons
`E = hv = (hc)/(lambda)`
`= (6.63 XX 10^(-34) j S) xx (3 XX 10^(8)m s^(-1))/(200 xx 10^(-9) m)`
`= 9.945 xx 10^(-19) J`
Using Einstien's photoelectric equation
`hv - KE + W`
or `KE = hv - W`
`= 9.945 xx 10^(-19) - 8.0 xx 10^(-19) = 1.945 xx 10^(-19) J`
`KE = (1)/(2) mv^(2) = 1.945 xx 10^(-19) J`
`("Mass of electron" = 9.1 xx 10^(-3)g)`
or `v = (2 xx 1.945 xx 10^(-19) J)/(9.1 xx 10^(-31))^(1//2)`
`= 6.54 xx 10^(6) m s^(-1)`