Example from Physics, 21.1 Planck and Quantum Nature of Light

How does Photon Energy Change with Various Portions of the EM Spectrum?

Refer to the Graphs of Blackbody Radiation shown in the first figure in this section. Compare the energy necessary to radiate one photon of infrared light and one photon of visible light.

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
To determine the energy radiated, it is necessary to use the equation $E = n h f .$ It is also necessary to find a representative frequency for infrared light and visible light.
Solution
According to the first figure in this section, one representative wavelength for infrared light is 2000 nm (2.000 × 10^-6 m). The associated frequency of an infrared light is

$f = \frac{c}{λ} = \frac{3.00 \times 10^{8} m / s}{2.000 \times 10^{- 6} m} = 1.50 \times 10^{14} H z .$
21.2

Using the equation $E = n h f$ , the energy associated with one photon of representative infrared light is

$\frac{E}{n} = h \cdot f = (6.63 \times 10^{- 34} J \cdot s) (1.50 \times 10^{14} Hz) = 9.95 \times 10^{- 20} \frac{J}{p h o t o n} .$
21.3

The same process above can be used to determine the energy associated with one photon of representative visible light. According to the first figure in this section, one representative wavelength for visible light is 500 nm.

$f = \frac{c}{λ} = \frac{3.00 \times 10^{8} m / s}{5.00 \times 10^{- 7} m} = 6.00 \times 10^{14} H z .$
21.4

$\frac{E}{n} = h \cdot f = (6.63 \times 10^{- 34} J \cdot s) (6.00 \times 10^{14} Hz) = 3.98 \times 10^{- 19} \frac{J}{p h o t o n} .$
21.5

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Strategy

Solution

Strategy

Solution