Example 29.4 from College Physics, 29.3 Photon Energies and the Electromagnetic Spectrum

How Many Photons per Second Does a Typical Light Bulb Produce?

Assuming that 10.0% of a 100-W light bulb’s energy output is in the visible range (typical for incandescent bulbs) with an average wavelength of 580 nm, calculate the number of visible photons emitted per second.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Power is energy per unit time, and so if we can find the energy per photon, we can determine the number of photons per second. This will best be done in joules, since power is given in watts, which are joules per second.
Solution
The power in visible light production is 10.0% of 100 W, or 10.0 J/s. The energy of the average visible photon is found by substituting the given average wavelength into the formula

$E = \frac{hc}{λ} .$
29.19

This produces

$E = \frac{(6 . 63 \times 10^{–34} J \cdot s) (3.00 \times 10^{8} m/s)}{580 \times 10^{–9} m} = 3.43 \times 10^{–19} J .$
29.20

The number of visible photons per second is thus

$photon/s = \frac{10.0 J/s}{3 . 43 \times 10^{–19} J/photon} = 2.92 \times 10^{19} photon/s .$
29.21
Discussion
This incredible number of photons per second is verification that individual photons are insignificant in ordinary human experience. It is also a verification of the correspondence principle—on the macroscopic scale, quantization becomes essentially continuous or classical. Finally, there are so many photons emitted by a 100-W lightbulb that it can be seen by the unaided eye many kilometers away.

0 of 3 steps open

How did it go?

Strategy

Solution

Discussion

Strategy

Solution

Discussion