Question

Calculate the value of the longest wavelength which can result in the emission of a photoelectron from sodium surface whose work function is 2.28 eV. (1 mark)
a.
544.1 nm
b.
5.441 nm
c.
54.41 nm
d.
542.1 nm

Answer 1

The longest wavelength which can result in the emission of a photoelectron from sodium surface whose work function is 2.28 eV, is

544.1 nm (option a.)

To understand this question, first, we need to know what do we mean by the work function of a metal. The work function of a metal is the minimum amount of energy to take out an electron from the orbital of an atom. The value of the work function is equal to the energy of the electron revolving around the nucleus. The formula for work function is,

$W = \frac{hc}{\lambda_{0} }$

where, h= planck's constant = $6.626*10^{-34}JHz^{-1}$

            c= speed of light = $3*10^{8}m/s$

            $\lambda_{0}$ = longest wavelength of photon

Given, $\lambda_0 = 2.28 eV =(2.28*1.6021*10^{-19}) J$

[Here longest wavelength of the photon would contribute to the shortest amount of energy (easier) needed to eject out the electron from the orbit.]

Therefore,

$W = \frac{hc}{\lambda_{0} }\\2.28*1.6021*10^{-19}=\frac{6.626*10^{-34}*3*10^{8}}{\lambda_{0} }\\\lambda_0 =544 nm$

Hence, the longest wavelength would be 544.1 nm.