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

Calculating the Number of Photons in a Laser Pulse

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

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

407 nm x 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 (λ)

E = (0.000000000000000000000000000000000663 Js) * 300,000,000 m/s = 1.989 × 10^-25 J/ms

E = 1.989 x 10^-25 J/ms / 4.07 x 10^-7 m = 4.8869779 x 10^-33 J (the meters cancel out)

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

0.897 J / 4.8869779 x 10^-33 J = ((0.897 J) / 4.8869779) * (10^(-33)) = 1.8343558 x 10^-34 photons

How is the number of photons produced in a laser pulse of 0.897 J at 407 nm calculated?

The number of photons produced in a laser pulse of 0.897 J at 407 nm is calculated by first determining the energy of a single photon using the formula E = hc/λ. After converting the given wavelength from nanometers to meters, the energy in Joules of a single photon is found to be 4.89 x 10^-33 J. By dividing the total energy of the laser pulse (0.897 J) by the energy of a single photon, we get the number of photons present in the pulse, which is approximately 1.8343558 x 10^-34 photons.