A helium-neon laser is pumped by electric discharge. What wavelength electromagnetic radiation would be needed to pump it? See Figure 30.39 for energy-level information.

Consider the formula for the energy of X ray photons as follows:

\({\bf{E = }}\frac{{{\bf{hc}}}}{{\bf{\lambda }}}\)

Here,

λ = Wavelength

E = Energy of the x-ray photons

h = Planck's constant

c = Speed of light

Consider the given data:

\(\begin{array}{l}h = 6.626 \times {10^{ - 34}}\;\;{\rm{J}} \cdot s\\E = 20.66\;{\rm{eV}}\\c = 3 \times {10^8}\;\frac{{\rm{m}}}{{\rm{s}}}\end{array}\)

Substituting the values in equation of energy.

\(\begin{array}{l}20.66\;{\rm{eV}} = \frac{{\left( {6.626 \times {{10}^{ - 34}}\;{\rm{J}} \cdot {\rm{s}}} \right)\left( {3 \times {{10}^8}\;\frac{{\rm{m}}}{{\rm{s}}}} \right)}}{\lambda }\\\lambda = \frac{{\left( {6.626 \times {{10}^{ - 34}}\;{\rm{J \times s}}} \right)\left( {3 \times {{10}^8}\;\frac{{\rm{m}}}{{\rm{s}}}} \right)}}{{20.66\;{\rm{eV}}}}\\\lambda = 60.18 \times {10^{ - 9}}\;{\rm{m}}\\\lambda = 60.18\;{\rm{nm}}\end{array}\)

Consider the wavelength of the electromagnetic radiation is 60.18 nm.