Question

How many photons are produced in a laser pulse of 0.897 J at 407 nm?

Answer 1

The relationship between energy of a single photon and its wavelength can be determined using the formula E=hc/lambda where E is energy, h is Planck's constant, c is the speed of light, and lambda is photons.

Before being able to solve for energy, need to convert nanometers to meters.

407 nm (1 m/1 x 10^9 nm) = 4.07 x 10^-7 m

Then plug in the values we know into the equation.
E h(Planck's constant) c(speed of light)
E = (6.63 x 10^-34 Js)(3 x 10^8 m/s) / 4.07 x 10^-7 m (lambda)

E=(0.000000000000000000000000000000000663js)(300,000,000m/s)=1.989×10^-25j/ms

E=1.989x10^-25j/ms /{divided by} 4.07x10^-7m = 4.8869779x10^-33 J (the meters cancel out)

E = 4.89 x 10^-33 J

This gives us the energy in Joules of a single photon. Now, we can find the number of photons in 0.897 J

0.897J / 4.89 x 10^-33 J = ((0.897 J) / 4.89) x ((10^(-33)) J) = 1.8343558 x 10^-34

1.83435583 × 10-34m4 kg2 / s4 photons