Question

What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337nm?

Short answer

Binding energy in eV of electrons in magnesium is 3.68eV

Step-by-step solution

Definition of Binding energy

Binding energy is the energy needed to disperse all of the particles in a system or remove a particle from it.

Determination of the binding energy

The wavelength of the photon is

λ= 337nm

= 337× 10^-19m

We also know:

h = 6.63×10^-34

c =3×10⁸ m/s

The energy of the photon is expressed as,

\(E=\frac{{hc}}{\lambda}\) ...(1)

Here, E is the binding energy, h is the plank constant,c is the speed of light and λ is the wavelength.

Substitute all the values in the above equation (1)(1), and we get:

\(\begin{aligned}E &= \frac{{\left( {6.62 \times {{10}^{ - 34}}\,{\rm{J \times s}}} \right)\left( {3\times{{10}^8}\,{{\rm{m}}\mathord{\left/{\vphantom{{\rm{m}} {\rm{s}}}} \right\{\rm{s}}}} \right)}}{{337\times{{10}^{-19}}\,{\rm{m}}}}\\&= 5.89 \times {10^{-19}}\,{\rm{J}} \times \frac{{1\,{\rm{eV}}}}{{1.60 \times {{10}^{-19}}\,{\rm{J}}}}\\&= 3.68\,{\rm{eV}}\end{aligned}\)

Hence the binding energy of the electrons in magnesium is 3.68eV .