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 MeV of a photon having a wavelength of 1.00 picometer.
We can call the photon wavelength of 1.00 picometer 𝜆. We want to solve for the photon’s energy; we’ll call that 𝐸. To start off, we can recall that the energy of a photon is equal to Planck’s constant times the frequency, which is equal to ℎ times 𝑐 over 𝜆.
Since we’ve been given the photon wavelength in our problem statement, we’ll use that form of the equation for photon energy. We’ll treat Planck’s constant ℎ as exactly 6.626 times 10 to the negative 34th joule seconds and the speed of light 𝑐 as 3.00 times 10 to the eighth meters per second.
When we plug these values into our equation for 𝐸, making sure to use a value in units of meters for our wavelength 𝜆, we also add in a conversion factor between units of energy, joules to electron volts. Using this conversion factor and entering these values on our calculator, we find the energy of the photon is 1.24 megaelectron volts. That’s the energy of a photon with a wavelength of 1.00 picometer.