Gwenno's camera sensor logs single photons. For one kind of light, every logged photon delivers exactly the same energy. She wants that number, in joules.
This lesson runs the photon-energy equation forward: frequency in, energy out. One multiply, with powers of ten riding along, and answers landing near 10⁻¹⁹ J.
The givens are always the same two: the light's frequency f, and Planck's constant h = 6.63 × 10⁻³⁴ J·s.
Take visible light with a frequency of 6.0 × 10¹⁴ Hz.
Multiply the number parts first: 6.63 × 6.0 = 39.78.
Combine the powers of ten: 10⁻³⁴ times 10¹⁴ makes 10⁻²⁰.
So E = 39.78 × 10⁻²⁰ J, which is written 3.978 × 10⁻¹⁹ J, and rounds to 3.98 × 10⁻¹⁹ J.
Check the size: one visible-light photon's energy sits near 10⁻¹⁹ J, a very small lump. An answer far from that size signals a powers-of-ten slip.
Units ride the final line, always: joules.
A photon of light has a frequency of 6.0 × 10¹⁴ Hz. Calculate the photon's energy, in joules.
Write down the values:
f = 6.0 × 10¹⁴ Hz, h = 6.63 × 10⁻³⁴ J·s, E = ?
Write down the equation:
E = hf
Substitute in the values, and calculate:
6.63 × 6.0 = 39.78, and the powers of ten combine: 10⁻³⁴ times 10¹⁴ makes 10⁻²⁰. So E = 39.78 × 10⁻²⁰ J, which rounds to 3.98 × 10⁻¹⁹ J.
The photon's energy is about 3.98 × 10⁻¹⁹ J.
Violet light has a frequency of 7.5 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules.
Write down the values:
f = 7.5 × 10¹⁴ Hz, h = 6.63 × 10⁻³⁴ J·s, E = ?
Write down the equation:
E = hf
Substitute in the values, and calculate:
6.63 × 7.5 = 49.725, and the powers of ten make 10⁻²⁰. So E = 49.725 × 10⁻²⁰ J, which rounds to 4.97 × 10⁻¹⁹ J.
The photon's energy is about 4.97 × 10⁻¹⁹ J.
A photon of deep red light has a frequency of 4.0 × 10¹⁴ Hz. Calculate its energy, in joules, to three significant figures.
A blacklight tube sends out ultraviolet light of frequency 8.0 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
A glow stick's light has a frequency of 5.2 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
A violet laser pointer sends out light of frequency 7.0 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
An ultraviolet sterilizing lamp sends out light of frequency 9.0 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
A red bicycle tail-light sends out light of frequency 4.6 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
A TV remote sends out infrared light of frequency 3.8 × 10¹⁴ Hz. Calculate the energy of one of its photons, in joules, to three significant figures.
A lamp shines on a sensor for 5.0 seconds. The light's frequency is 6.8 × 10¹⁴ Hz. Calculate the energy of one photon of this light, in joules, to three significant figures.
A photon of visible light lands on a sensor. Which is the right size for the energy it delivers?