Question

What is the wavelength of the electromagnetic radiation needed to eject electrons from a metal?

Answer 1

Answer:

λ = hc/(eV + h$f_{0}$)

Explanation:

Let the work function of the metal = ∅

the kinetic energy with which the electrons are ejected = E

the energy of the incident electromagnetic wave = hf

Then, we know that the kinetic energy of the emitted electron will be

E = hf - ∅

because the energy of the incident electromagnetic radiation must exceed the work function for electrons to be ejected.

This means that the energy of the incident e-m wave can be written as

hf = E + ∅

also, we know that the kinetic energy of the emitted electron E = eV

and the work function ∅ = h$f_{0}$

we can they combine all equations to give

hf = eV + h$f_{0}$

we know that f = c/λ

substituting, we have

hc/λ = eV + h$f_{0}$

λ = hc/(eV + h$f_{0}$)    This is the wavelength of the e-m radiation needed to eject electrons from a metal.

where

λ is the wavelength of the e-m radiation

h is the Planck's constant = 6.63 x 10^-34 m^2 kg/s

c is the speed of e-m radiations in a vacuum = 3 x 10^8 m/s

e is the charge on an electron

V is the voltage potential on the electron

$f_{0}$ is the threshold frequency of the metal