Question

What is the maximum velocity of an electron emitted from the surface of a metal whose work function is 5 eV, if the metal is illuminated by light of wavelength is 200 nm?  

Answer 1

Energy of light having frequency (or wavelength ) is given by,

Where,

h=6.63×10^-34 J-s (Planck's constant)

c=3×10⁸ m/s (speed of light)

Work function of a metal (W) is define as the minimum energy required to extract electron from the metal.

When we shine light on a metal, some energy is used as work function and the rest of the energy will be as kinetic energy of electron.

So using energy conservation,

Given:

W= 5 eV = 5×1.6×10^-19 J = 8×10^-19 J

Energy of light,

So kinetic energy,

KE=E-W = (9.945-8)×10^-19 = 1.945×10^-19 Joule

If m is the mass and v is the speed of electron then kinetic energy is given by,

Mass of electron m=9.1×10^-31 Kg

So speed of electron,

This will be the maximum velocity as we have neglected collision between electrons. If collision is also there, speed gets decreased due to collision.

If you have any doubt, feel free to discuss in the comments.