Max Planck was awarded the Nobel Peace Prize in 1918 for his discovery of energy quanta. He suggested in 1900 that electromagnetic energy was emitted in quantized packets of energy. He was able to postulate that the energy in a photon. It was only later that the postulate because the accepted calculation.
Energy In a Photon
\(\large\mathsf{ E = hf }\)
... where E is the energy, h is Planck's energy constant of 6.626 x 10-34 J·s, and f is the frequency of the light.
Use the energy equation to solve each of the problems on the tabs below. Once you have solved them on your own, press the Answer button to check your work. Keep in mind that energy is often shown in electron-volts (eV). 1 eV is equal to 1.6 x 10-19 J, so you may have to convert to Joules from electron-volts and vice versa.
Green Light
Yellow Light
Red Light
The frequency of green light is 5.45 x 1014 Hz. How much energy does a photon of green light carry?
\(\mathsf{ E = hf }\)
\(\mathsf{ E = 6.626 \times 10^{-34} \text{ J·s} \cdot 5.45 \times 10^{14} \text{ Hz} }\)
\(\mathsf{ E = 3.61 \times 10^{-19} \text{ J} }\)
OR
\(\mathsf{ E = \frac{3.61 \times 10^{-19} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} = 2.26 \text{ eV} }\)
A photon of yellow light has 2.15 eV of energy. What is the frequency of yellow light?
\(\mathsf{ E = 2.15 \text{ eV} \cdot 1.6 \times 10^{-19} \text{ J/eV} = 3.44 \times 10^{-19} \text{ J}}\)
\(\mathsf{ 3.44 \times 10^{-19} \text{ J} = 6.626 \times 10^{-34} \text{ J·s} \cdot f }\)
\(\mathsf{ f = \frac{3.44 \times 10^{-19} \text{ J}}{6.626 \times 10^{-34} \text{ J·s}} }\)
\(\mathsf{ f = 5.19 \times 10^{14} \text{ Hz} }\)
The frequency of red light is 4.00 x 1014 Hz. How much energy does a photon of red light carry?
\(\mathsf{ E = hf }\)
\(\mathsf{ E = 6.626 \times 10^{-34} \text{ J·s} \cdot 4.00 \times 10^{14} \text{ Hz} }\)
\(\mathsf{ E = 2.65 \times 10^{-19} \text{ J} }\)
OR
\(\mathsf{ E = \frac{2.65 \times 10^{-19} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} = 1.66 \text{ eV} }\)
