← The photon model

The photon-energy equation

Hamish wants a number. A single photon lands on a light sensor and delivers its whole lump. Exactly how much energy was that, in joules?

A photon's energy rises in proportion with frequency; that was the direction. This lesson presents the exact rule, which turns a frequency such as 5.0 × 10¹⁴ Hz into one photon's energy.

The photon-energy equation is E = hf.

E is the photon's energy, measured in joules (J).

sensorfrequency 5.0 × 10¹⁴ HzE = ?
One photon, one frequency: the equation turns the frequency into the energy.

f is the light's frequency, measured in hertz (Hz).

h is a fixed number of nature, the same for every photon of every kind of light.

That fixed number is called Planck's constant, and its value is h = 6.63 × 10⁻³⁴ J·s.

E = hfEthe photon's energyjoules (J)fthe light's frequencyhertz (Hz)hPlanck's constant6.63 × 10⁻³⁴ J·s
Each symbol, its meaning, and its unit.

You have met the letter h before: in the work and energy topic, h stood for an object's height. Here h is Planck's constant, not a height. Any problem that needs both writes 'height' out in words.

the letter hthis topicPlanck's constant, a fixed number of naturethe work and energy topican object's height, written out as 'height' when both appear in one problem
Two jobs for one letter: here, h is Planck's constant, never a height.

Multiplying the light's frequency by Planck's constant gives one photon's energy. That is all E = hf says. The multiplying itself is the next lesson's job; this lesson's job is the equation and its parts.

Which of these is the photon-energy equation: E = hf, E = h + f, or h = Ef?

A photon's energy rises in proportion with frequency, so the right form multiplies f by a fixed constant.

E = h + f adds unlike quantities; adding joule-seconds to hertz has no meaning.

h = Ef puts the fixed constant on the left as if it were the unknown; h never changes.

E = hf is the photon-energy equation.

In E = hf, which symbol carries the unit hertz, and which carries joules?

f is the light's frequency, so f carries hertz.

E is the photon's energy, so E carries joules.

h is Planck's constant, in joule-seconds, which ties the two together.

f is in hertz; E is in joules.

Which equation gives a photon's energy from the light's frequency?

In the equation E = hf, which quantity is measured in hertz?

The fixed number h in the photon-energy equation is called which of the following?

Your turn

Which equation is the photon-energy relation?

Which line pairs each symbol in E = hf with its unit correctly?

A problem needs Planck's constant and a shelf's height at the same time. How is the height written?