The higher the frequency ν (cycles per second, or Hertz) the shorter the wavelength λ (length per cycle), and the greater the energy per photon. Since wavelength and frequency are inversely related (as one goes up the other goes down), so energy is directly related to frequency by the relationship E = hν or inversely related to the wavelength E= hc/λ, where h is Planck’s constant. So radiation with a very short wavelength, such as X-rays (λ= ~10^-10 m) and ultraviolet light (between 10^-7 to 10^-8 m) have much more energy per particle than long wavelength radiation like radio and microwaves (λ= ~10³ m). This is why we don’t mind being surrounded by radio waves essentially all the time yet we closely guard our exposure to gamma-rays, X-rays and UV light; their much higher energies cause all kinds of problems with our chemistry, as we will see later.

Because of the relationship between energy and wavelength, you can shine light of long wavelength (low energy - such as infrared light) but high intensity (many photons per second) on a metal plate and no electrons will be released. But shine low intensity (few photons per second), high energy, short wavelength light, such as ultraviolet light or X-rays, on the plate and electrons are ejected. Once the wavelength is short enough to eject electrons, increasing the intensity of the light increases the number of electrons emitted. An analogy is with a vending machine that can only recognize quarters, you could put many nickels or dimes into the machine all day and nothing will come out. The surprising result is that the same total amount of energy can produce very different effects. Einstein explained this observation by assuming that only photons with “enough” energy could eject an electron from an atom; if photons with less energy hit the atom, no matter how many, no electrons are ejected58. Enough energy for what, you might ask, and the answer is that the lower energy photons simply do not have enough energy to overcome the attraction between an electron and the nucleus. Recall that, in the photoelectric effect, each photon ejects an electron from an atom on the surface of the metal. The electrons are somewhere in the atom (we have not yet specified where), but it takes energy to remove them, and the energy is used to overcome the attraction of the negative electron and the positive nucleus.

Now you should be really confused (a normal reaction)! On one hand we were fairly convinced that light acted as a wave, but now we see some of its behaviors can be best explained in terms of particles. This dual nature of light is conceptually difficult for most (normal) people because it is completely counterintuitive. In our macroscopic (normal) world things are either particles (bullets, balls, coconuts) or waves (in water), they are not, no not ever, both. As we will see, electromagnetic radiation is not the only example of something that has the properties of both a wave and a particle (or wave-particle duality as it is known) - electrons, protons, and neutrons also display wave-like properties. In fact, all matter has a wavelength, defined by Louis de Broglie (1892-1987) by the equation λ = h/mν, where mv is the object’s momentum and h is Planck’s constant (again).