How many photons are produced in a laser pulse of 0.528 J at 679 nm?

Every photon has a characteristic energy associated with it. The energy of a photon is dependent on its frequency. The way I would solve this is to convert the wavelength, 679 nm, to a frequency and then find the energy. After we know the energy of a single photon, we can find out how many it takes to get the total energy of the pulse (0.528 J).

Some useful equations:

λν = c

Wavelength, λ (lambda), times frequency, ν (nu), equals the speed of light.

c = 3.0 x 10^{8} m/s.

E = hν

Energy of a single photon is the product of Planck's constant, h, and the frequency, ν. h = 6.63 x 10^{-34} J•s.

I prefer to manipulate the equations before plugging in our known values.

We have a wavelength as a known, so let's solve for the energy of a single photon at that wavelength:

λν = c

ν = c/λ

Plug this into the other equation:

E = hν

E = hc/λ

Now we can plug in our two constants (h and c, they never change) and our known (λ = 679 nm = 679 x 10^{-9} m) and find the energy of a single photon. Make sure you use the value of the wavelength in meters (679 x 10^{-9} m).

E = 2.93 x 10^{-19}

Let's check our units:

h is in J•s (energy • time). c is in m/s (distance/time). Wavelength is in m (after we converted from nm).

So our final units should be: (J•s•m/s)/m = (J•s•m/s)/m = (J•m)/m = J

Good, that is what we wanted.

Each photon of light at 679 nm is 2.93 x 10^{-19} J of energy. The whole pulse is 0.528 J. It is a simple matter of division to get:

0.528 J / 2.93 x 10^{-19} J = 1.8 x 10^{18} photons

We divided the energy of the whole pulse by the energy per photon to get the number of photons.

Feel free to comment on the areas which are confusing. Good luck.

## Comments

In case you are used to seeing the conversion in more of a grid, here is the very last step.

The problem said you have a pulse of 0.528 J, and Robert did all the calculations and got to the fact that each 1 photon is equivalent to 2.93 x 10-19 J.

0.528 J x 1 photon = 1.8 x 10

^{18}photons2.93 x 10-19 J

Thank you both.

You are welcome.