# How do you calculate the number of photons?

Aug 22, 2014

You calculate the energy of a photon, and then you use the total energy to calculate the number of photons.

To calculate the energy of a photon, see How do you calculate the energy of a photon of electromagnetic radiation?.

Then

Number of photons = $\text{Total energy"/"Energy of one photon}$

Few instructors will make the question so simple. Instead, they might disguise it as follows.

EXAMPLE

A common laser pointer produces 1.0 mW at a wavelength of 670 nm. Calculate the number of photons produced per millisecond.

Solution

Step 1. Calculate the energy of a photon.

E = (hc)/λ = (6.626 × 10^34"J·s" × 2.998 × 10^8"m·s"^-1)/(670 × 10^-9"m") = 2.965 × 10^-19 "J"

( 3 significant figures + 1 guard digit)

Step 2. Calculate the total energy per second.

Total energy = 1.0 × 10^-3"W" × (1"J·s"^-1)/(1"W") = 1.0 × 10^-3 "J·s"^-1

Step 3. Calculate the number of photons per millisecond.

Number of photons =

"Total energy"/"Energy of one photon" = 1.0 × 10^-3 "J·s"^-1 × (1"photon")/( 2.965 × 10^-19"J") ×

(1"s")/(1000"ms") = 3.4 × 10^12 "photons/ms"