Example from Physics, 21.1 Planck and Quantum Nature of Light

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

Assuming that 10 percent 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
The number of visible photons per second is directly related to the amount of energy emitted each second, also known as the bulb’s power. By determining the bulb’s power, the energy emitted each second can be found. Since the power is given in watts, which is joules per second, the energy will be in joules. By comparing this to the amount of energy associated with each photon, the number of photons emitted each second can be determined.
Solution
The power in visible light production is 10.0 percent 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

$E = n h f = \frac{n h c}{λ} .$
By rearranging the above formula to determine energy per photon, this produces

$E / n = \frac{(6.63 \times 10^{- 34} J \cdot s) (3.00 \times 10^{8} m / s)}{580 \times 10^{- 9} m} = 3.43 \times 10^{- 19} J / p h o t o n .$
21.1

The number of visible photons per second is thus

$\frac{p h o t o n s}{sec} = \frac{10.0 J / s}{3.43 \times 10^{- 19} J / p h o t o n} = 2.92 \times 10^{19} p h o t o n s / s.$

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