In 1905, Einstein published his initial paper on the theory of relativity, the subject for which he is most well known to the general public. He also published another paper, on the nature of light. In it Einstein offered an exceedingly simple but amazingly bold idea to explain Lenard’s photoelectric-effect data.

A few years earlier, in 1900, the German physicist Max Planck had been trying to understand the details of the rainbow-like blackbody spectrum of light emitted by a glowing hot object. As we noted in the preceding chapter, this problem didn’t yield to a classical physics analysis, but Planck found that he could calculate the spectrum perfectly if he made an unusual assumption. The atoms in a solid vibrate back and forth around their equilibrium positions with frequency $f$. You learned in Chapter 15 that the energy of a simple harmonic oscillator depends on its amplitude and can have any possible value. But to predict the spectrum correctly, Planck had to assume that the oscillating atoms are not free to have any possible energy. Instead, the energy of an atom vibrating with frequency $f$ has to be one of the specific energies $E=0\text{,}hf\text{,}2hf\text{,}3hf\text{,}\dots$, where $h$ is a constant. That is, the vibration energies are quantized.

Planck was able to determine the value of the constant $h$ by comparing his calculations of the spectrum to experimental measurements. The constant that he introduced into physics is now called Planck’s constant. Its contemporary value is

The first value, with SI units, is the proper one for most calculations, but you will find the second to be useful when energies are expressed in eV.

Einstein was the first to take Planck’s quantization idea seriously. He went even further and suggested that electromagnetic radiation itself is quantized! That is, light is not really a continuous wave but, instead, arrives in small packets or bundles of energy. Einstein called each packet of energy a light quantum, and he postulated that the energy of one light quantum is directly proportional to the frequency of the light. That is, each quantum of light has energy

where $h$ is Planck’s constant and $f$ is the frequency of the light.

The idea of light quanta is subtle, so let’s look at an analogy with raindrops. A downpour has a torrent of raindrops, but in a light shower the drops are few. The difference between “intense” rain and “weak” rain is the rate at which the drops arrive. An intense rain makes a continuous noise on the roof, so you are not aware of the individual drops, but the individual drops become apparent during a light rain.

Similarly, intense light has so many quanta arriving per second that the light seems continuous, but very weak light consists of only a few quanta per second. And just as raindrops come in different sizes, with larger-mass drops having larger kinetic energy, higher-frequency light quanta have a larger amount of energy. Although this analogy is not perfect, it does provide a useful mental picture of light quanta arriving at a surface.