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Set 57 Problem number 13


Problem

How many electron volts of energy are associated with a single atomic mass unit, or amu (an amu is approximately 1.66 * 10^-27 kg)? How many electron volts are associated with the mass of an electron (electron mass approximately 9.11 * 10^-31 kg)? What would be the wavelength of a single photon with this energy? Compare each wavelength with the diameter of a typical atom, which is 10^-10 m or 1 Angstrom, and with the diameter of a typical proton, which is about 10^-15 m or 1/100,000 Angstrom; this distance is also called a Fermion.

Solution

The energy equivalent of 1 amu is

1.5 * 10^-10 J / ( 1.6 * 10^-19 J / eV) = 9.3 * 10^8 eV, or 930 million electron volts (930 meV).

The energy equivalent of an electron mass is

8.2 * 10^-14 J / ( 1.6 * 10^-19 J / eV) = 510 * 10^8 eV, or 510 thousand electron volts (510 keV).

The photon wavelengths will are found from E = hf = h c / `lambda to be `lambda = h c / E for the corresponding energies:

and

Photons of these wavelengths can occur in particle accelerators and in cosmic rays.  The energy of such photons can in various interactions convert its form into a combination of mass and energy, with the energy manifesting itself in the form of kinetic energy of massive particles and/or in the energy of lower-frequency photons.

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