38.3.2 The Photon Rate

Light, in the raindrop analogy, consists of a stream of photons. For monochromatic light of frequency $f, N$ photons have a total energy $E_{light} = N h f$ . We are usually more interested in the power of the light, or the rate (in joules per second, or watts) at which the light energy is delivered. The power is

P = \frac{d E_{light}}{d t} = \frac{d N}{d t} h f = R h f

(38.10)

where $R = d N / d t$ is the rate at which photons arrive or, equivalently, the number of photons per second.

EXAMPLE 38.5 The photon rate in a laser beam

The 2.0 mW light beam of a red laser pointer $(λ = 650 nm)$ shines on a screen. How many photons strike the screen each second?

MODEL Use the photon model of light.

SOLVE The light-beam power, or energy delivered per second, is $P = 2.0 mW = 0.0020 J/s$ . The frequency of the light is $f = c / λ = 4.61 \times 10^{14} Hz$ . The number of photons striking the screen per second, which is the rate of arrival of photons, is

R = \frac{P}{h f} = 6.5 \times 10^{15} photons per second

REVIEW That is a lot of photons per second. No wonder we are not aware of individual photons!