Answer to Question #153797 in Atomic and Nuclear Physics for Vanshika Gupta

Question

How is the energy of a photon dependent on the frequency and wavelength? Based on that, how many photons are emitted in a nitrogen gas laser pulse with a wavelength of 337 nm and energy of 3.83 mJ?

Answer 1

$E = hν = \frac{hc}{λ} \\ λ = 337 \; nm \\ E_{total} = 3.83 \; mJ \\ E = \frac{hc}{λ} \\ = \frac{6.626 \times 10^{-34} \times 3 \times 10^8 }{337 \times 10^{-9}}$

$= 58.9852 \times 10^{-20} \;J$ (energy of one photon)

Number of photons:

$N = \frac{E_{total}}{E} \\ = \frac{3.83 \times 10^{-3}}{58.9852 \times 10^{-20}} \\ = 6.4932 \times 10^{15} \;photons$

Answer: $6.4932 \times 10^{15} \;photons$