17.2.1 Photon Model of Light

Since the wave model of light cannot square with these three experimental observations, perhaps light is not a wave after all? If not a wave, then what?

In 1805, Albert Einstein made the bold hypothesis that light consists of a stream of particles called photons. He described a photon as a packet of electromagnetic radiation energy. And the amount of energy in each packet is proportional to the frequency (and thus inversely proportional to the wavelength) of the EM radiation

$\displaystyle E=hf=\frac{{hc}}{\lambda }$

The symbol h denotes the Planck’s constant, which has a tiny value of $\displaystyle h=6.63\times {{10}^{{-34}}}\text{ J s}$ . So a photon (even for very high frequency EM radiation like X-rays and gamma rays) is a tiny packet of energy.

To familiarise ourselves with Einstein’s idea, let’s contrast the photon model with the wave model.

Monochromatic

The wave model says that a beam of monochromatic light is a light wave with a single frequency. The photon model says that it is a stream of photons of a single photon energy $\displaystyle E=hf$ . Note also that a light wave delivers energy in a wave-like manner, which is continuous over time and spread over space. But a stream of photons delivers energy in a particle-like manner, which is “lumpy” and “spotty”.

Intensity

As a wave, increasing the light intensity is to increase the amplitude of the wave. As photons, increasing the light intensity is to increase the number of photons (per unit time per unit area) in the beam.

Frequency

Based on the wave model, blue light is a wave with a higher frequency (and shorter wavelength) than red light. Based on the photon model, blue light consists of more energetic photons than red light. In other words, red light delivers energy in larger instalments than red light.

It may take a while to wrap your head around the new meaning of frequency. It has the unit of Hz, but there is nothing “oscillating” or “per second” about it. It may sound like a whimsical theory at first, but as you shall see, the photon theory is totally supported by experimental results. And that’s all that matters in science.

Example

A beam of monochromatic red light of wavelength 750 nm is delivering 5.0 W of power to an emitter plate. Calculate the rate of arrival of photons N_t at the emitter.

Solution

$\displaystyle {{E}_{{red}}}=\frac{{hc}}{\lambda }=\frac{{(6.63\times {{{10}}^{{-34}}})(3.00\times {{{10}}^{8}})}}{{750\times {{{10}}^{{-9}}}}}=2.652\times {{10}^{{-19}}}\text{ J}=1.7\text{ eV}$

$\displaystyle \begin{aligned}P&={{N}_{t}}\frac{{hc}}{\lambda }\\5.0&={{N}_{t}}(2.652\times {{10}^{{-19}}})\\{{N}_{t}}&=1.89\times {{10}^{{19}}}\text{ }{{\text{s}}^{{-1}}}\end{aligned}$