Question

In the 1980s, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in \({\bf{MeV}}\)of a photon having a wavelength of a picometer.

Short answer

Find the energy in MeV of a photon having a wavelength of a picometer is \(1.24\,MeV\).

Step-by-step solution

Definition of wavelength

The distance between successive crests of a wave, particularly in a sound or electromagnetic wave.

Find the energy in \({\bf{MeV}}\) of photon

Consider the given problem and solve.

A photon having a wavelength of a picometer \(\left( {\lambda = {{10}^{12}}\;{\rm{m}}} \right)\) carries the energy of:

\(\begin{aligned} E &= \frac{{hc}}{\lambda }\\ &= \frac{{6.626 \cdot {{10}^{34}}\,{\rm{Js}} \cdot 3 \cdot {{10}^8}\,\frac{{\rm{m}}}{{\rm{s}}}}}{{{{10}^{12}}\;{\rm{m}}}}\\ &= 1.99 \cdot {10^{13}}\;{\rm{J}}\,\frac{{6.24 \cdot {{10}^{18}}\,{\rm{eV}}}}{{\rm{J}}}\\ &= 1.24\,{\rm{MeV}}\end{aligned}\)

Therefore the calculated energy in \(MeV\) is \(1.24\,MeV\).