Question

Two metals x and y have work functions 2ev and 5ev respectively. Which metal will emit electrons when irradiated with the light of wavelength 400 nm

Answer 1

Answer:- Metal x will emit electrons when irradiated with the light of wavelength 400 nm.

Solution:- An electron from a metal surface could only be emitted if the energy of the light photon is equal to or greater than the work function of the metal. So, let's calculate the work function for the given wavelength and see which metal would emit the electron.

$E=\frac{hc}{\lambda }$

Where E is the energy, h is planck's constant and c is the speed of light.

Convert given wavelength from 400 nm to m and plug in the values in the equation.

since, $1nm=10^-^9m$

So,  $400nm(\frac{10^-^9m}{1nm})$

= $4*10^-^7m$

$E=\frac{6.626*10^-^3^4J.s(3*10^8m.s^-^1)}{4*10^-^7m}$

E = $4.97*10^-^1^9J$

Convert J to eV.

Since, $1eV=1.60*10^-^1^9J$

So, $4.97*10^-^1^9J(\frac{1eV}{1.60*10^-^1^9J})$

= 3.10eV

Calculated energy of the light photon is 3.10 eV which is greater than the work function of metal x and less than of metal y. So, it is only metal x that will emit the electrons.