Question

how many photons are produced in a laser pulse of 0.439 j at 515 nm? report your answer using 3 significant figures.

Explanation:

Step1: Calculate the energy of a single photon

The energy of a photon is given by the formula \(E = h
u\), where \(h\) is Planck's constant (\(h=6.626\times 10^{-34}\space J\cdot s\)) and \(
u\) is the frequency of the photon. The frequency \(
u\) and the wavelength \(\lambda\) are related by the equation \(
u=\frac{c}{\lambda}\), where \(c = 3\times 10^{8}\space m/s\) is the speed of light. Given \(\lambda=515\space nm = 515\times 10^{-9}\space m\), then \(
u=\frac{3\times 10^{8}}{515\times 10^{-9}}\space Hz\approx5.825\times 10^{14}\space Hz\).
The energy of a single photon \(E = h
u=6.626\times 10^{-34}\times5.825\times 10^{14}\space J\approx3.86\times 10^{-19}\space J\)

Step2: Calculate the number of photons

If the total energy of the laser pulse is \(E_{total}=0.439\space J\), and the energy of a single photon is \(E\), then the number of photons \(n=\frac{E_{total}}{E}\)
\(n=\frac{0.439}{3.86\times 10^{-19}}=\frac{0.439\times10^{19}}{3.86}\approx1.14\times 10^{18}\)

Answer:

\(1.14\times 10^{18}\)