## Mass and Energy

In 1900 Max Planck demonstrated that the energy (E) of electromagnetic radiation was simply related to the frequency of the radiation (u) by a constant (Planck's constant, h):

In addition, experiments indicated that the radiation was only released in discrete "bursts". This was a startling result as it departed from the classical assumption of continuous energy to one in which electromagnetic radiation could only exist in integral multiples of the product of hu. The radiation was said to be quantized, and the discrete quanta became known as photons. Each photon contained an amount of energy that was an integer multiple of hu. The unit for energy is the joule (J), and we can calculate the energy of the radiation contained in a photon of wavelength of, for example, 450 nm as:

450 X 10-9m

This radiation (450 nm) corresponds to the portion of the visible spectrum towards the ultraviolet end. Each photon of light at 450 nm contains the equivalent of 4.42 X 1019 J of energy in a discrete burst. We shall see the significance of this result later in this chapter when we discuss the emission of photons from scintillators.

The joule is the Système International d'Unites (abbreviated SI) unit of energy, however, a derived unit used frequently in discussions of the energy of electromagnetic and particulate radiation is the electron volt (eV). The electron volt is defined as the energy acquired when a unit charge is moved through a potential difference of one volt. Energy in joules can be converted to energy in electron volts (eV) by dividing by the conversion factor 1.6 X 1019 J.eV-1. Thus, the energy in eV for photons of 450 nm would be:

4.42 X 1019J

X rays and gamma rays have energies of thousands to millions of electron volts per photon (Fig. 2.2).

Einstein's Special Theory of Relativity, published in 1905 while he was working in the patent office in Zurich, turned the physical sciences on its head. It predicted, amongst other things, that the speed of light was constant for all observers independent of their frame of reference (and therefore that time was no longer constant), and that mass and energy were equivalent. This means that we can talk about the rest-mass equivalent energy of a particle, which is the energy that would be liberated if all of the mass were to be converted to energy. By rest mass we mean that the particle

Wavelength (m)

I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—r

Wavelength (m)

I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—r

 "v Short wave J Y rays I X rays radio Long wave Mic owaves radio Infrared |uv

Energy (eV)

Figure 2.2. The electromagnetic spectrum showing the relationship between wavelength, frequency, and energy measured in electron volts (eV).

is considered to be at rest, i.e., it has no kinetic energy. Consider the electron, which has a rest mass of 9.11 x 10-31 kg; we can calculate the amount of energy this mass is equivalent to from:

= 9.11 x 10-31kg x (3 x 108)2 m.s-1 = 8.2 x 10-14J 8.2 x 10-14J

The reader may recognize this as the energy of the photons emitted in positron-electron annihilation.