A diode laser emits a wavelength of 987 nm. All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?

8.04 × 10¹⁶ photons per second

Explanation:

First, we calculate the energy per photon from E = hc/λ where h = Planck's constant = 6.63 × 10⁻³⁴ Js c = speed of light = 3 × 10⁸ m/s and λ = wavelength of laser = 987 nm = 987 × 10⁻⁹ m = 9.87 × 10⁻⁷ m

So, E = hc/λ = 6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s/9.87 × 10⁻⁷ m = 19.89/9.87 × 10⁻¹⁹ J = 2.02 × 10⁻¹⁹ J per photon.

Since we have a total of 0.52 J over a period of 32 s, the output power is 0.52 J/32 s = 0.0163 J/s.

Thus the total number of photons per second is thus in output power/energy per photon = 0.0163 J/s ÷ 2.02 × 10⁻¹⁹ J per photon

= 8.04 × 10¹⁶ photons per second

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