Total energy = power x time
From the information given,
power = 4.6 watts
time = 16.38 s
Total energy = 4.6 x 16.38 = 75.348 J
The formula for calculating the energy of a photon is expressed as
E = hc/λ
where
h is the plank's constant and its value is 6.63 x 10^- 34 Js
c is the frequency of light and its value is 3 x 10^8 m/s
λ is the wavelength
From the information given,
λ = 689.12 x 10^- 9 m
Thus,
E = (6.63 x 10^- 34 x 3 x 10^8)/689.12 x 10^- 9
E = 28.86 x 10^-20 J
Number of photons = total energy/energy per photon
Number of photons = 75.348/28.86 x 10^-20
Number of photons = 2.61 x 10^20 photons