The work function for caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.

The work function for caesium atom is 1.9 eV. Calculate (a) the thresh

1.	The work function for caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.
Answer» Solution :(a) WORK function `(W_(0)) = h v_(0)` `:. v_(0) = (W_(0))/(h) = (1.9 xx 1.602 xx 10^(-19)J)/(6.626 xx 10^(-34) Js) = 4.59 xx 10^(14) s^(-1) (1 EV = 1.602 xx 10^(-19)J)` (B) `lamda_(0) = (c)/(v_(0)) = (3.0 xx 10^(8) ms^(-1))/(4.59 xx 10^(14) s^(-1)) = 6.54 xx 10^(-7) m = 654 xx 10^(-9) m = 654nm` (c) K.E. of ejected electron `= h (v - v_(0)) = hc ((1)/(lamda) - (1)/(lamda_(0)))` `= (6.626 xx 10^(-34) Js) (3.0 xx 10^(8) ms^(-1)) ((1)/(500 xx 10^(-9) m) - (1)/(654 xx 10^(-9) m))` `= (6.626 xx 3.0 xx 10^(-26))/(10^(-9)) ((154)/(500 xx 654)) J = 9.36 xx 10^(-20)J` K.E. `= (1)/(2) mv^(2) =9.36 xx 10^(-20) J or kg m^(2) s^(-2)` `:. (1)/(2) xx (9.11 xx 10^(-31) kg) v^(2) = 9.36 xx 10^(-20) kg m^(2) s^(-2)` or `v^(2) = 2.055 xx 10^(11) m^(2) s^(-2) = 20.55 xx 10^(10) m^(2) s^(-2) or v = 4.53 xx 10^(5) ms^(-1)`