The Planck constant

Q: What is the value of the Planck constant?

6.62607015 × 10⁻³⁴ J s. Since 20 May 2019 h is exactly 6.62607015 × 10⁻³⁴ J s. Before that, Kibble balances and counting the atoms in a silicon sphere measured it to about 10 parts per billion, and that value was frozen in.

Why does light come in tiny packets, and how big is one?

h = 6.626\,070\,15 \times 10^{-34}\ \text{J\,s}

Exact, by definition, since 2019 13 min read, with an experiment to run

Light looks smooth, but it arrives in tiny lumps of energy called photons. The Planck constant, $h$ , says how big each lump is: a photon's energy is $h$ times its frequency.

It is the founding number of quantum physics. It decides the colours of LEDs, how solar panels work and why atoms do not collapse. Since 2019 it also defines the kilogram.

1 · Play first

Shine light on metal and stop the electrons

Light hitting a clean metal can knock electrons out: the photoelectric effect. Dim red light never does it, however bright. Blue or ultraviolet does, even when faint.

Pick a metal, change the colour, and find the stopping voltage that just stops the fastest electrons. Plot a few colours and the slope of the line, times $e$ , is $h$ .

What to notice

Below a certain frequency no electrons come out, however bright the light.
Brighter light gives more electrons, not faster ones.
Every metal gives a line with the same slope. Only where it starts changes.

2 · The equation, piece by piece

Einstein's 1905 explanation: each photon gives all its energy to one electron. Some is spent escaping the metal, and the rest is left as movement, which the stopping voltage measures. Tap any piece.

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e V_s

Electron's leftover energy

The electron charge times the stopping voltage.

Robert Millikan set out to prove Einstein wrong. By 1916 his careful measurements had confirmed the straight line and gave $h$ to within about 0.5%.

3 · How we found it

1The glowing oven problem

In 1900 physics could not explain the colours of a hot oven. Theory said it should blaze with endless ultraviolet. Max Planck fixed the maths by assuming energy came in lumps of $hf$ . He thought it was a trick.

2Light is lumpy

In 1905 Einstein took the lumps seriously: light itself is made of photons. That explained why red light cannot free electrons, however bright, and won him the Nobel Prize.

In 1913 Niels Bohr used $h$ to explain why atoms give off sharp colours, and quantum mechanics grew from there.

3Holding up the kilogram

For 130 years the kilogram was a metal cylinder in a vault near Paris. Kibble balances measure mass with electrical power, which depends on $h$ . In 2019 $h$ was fixed and the kilogram is now defined from it.

1887
Hertz notices ultraviolet light helps sparks jump.
1900
Planck introduces $h$ to explain the glow of hot objects.
1905
Einstein explains the photoelectric effect with photons.
1913
Bohr uses $h$ to explain the hydrogen atom.
1916
Millikan's measurements confirm Einstein's line.
2019
$h$ is fixed exactly and the kilogram is redefined from it.

4 · How the value is pinned down

Since 20 May 2019 $h$ is exactly 6.62607015 × 10⁻³⁴ J s. Before that, Kibble balances and counting the atoms in a silicon sphere measured it to about 10 parts per billion, and that value was frozen in.

Now a Kibble balance does the reverse job. It uses the fixed $h$ to measure a mass.

5 · What if it were different?

If h were bigger

Quantum blurriness would show up at human scale, and a thrown ball might not have one clear path.

If h were zero

Atoms would collapse in a flash of light, and there would be no chemistry and no stable matter.

Why it matters to you

Every LED, camera sensor and solar panel is designed around photons of energy $hf$ .

6 · Try it at home

Find h with LEDs

An LED only lights once each electron crossing it gets enough energy to make one photon of its colour. So the switch-on voltage times $e$ is about $hf$ .

You need

Red, green and blue LEDs
A 9 V battery and a 1 kΩ variable resistor (potentiometer)
A multimeter

Do this

Wire the battery through the potentiometer to the LED, with the multimeter across the LED.
In a dark room, turn the voltage up slowly until the LED just starts to glow. Write down the voltage.
Do the same for each colour.
Look up each LED's wavelength (about 630 nm red, 525 nm green, 470 nm blue) and work out $f = c/\lambda$ .

The maths

Each LED gives $h \approx eV/f$ . For red, $1.8 \times 1.6\times10^{-19} / 4.8\times10^{14} \approx 6\times10^{-34}$ J s. Expect to be within 20% or so: LEDs are not perfect.

Stay safe: Always keep the resistor in the circuit. An LED straight across a battery can burn out or get hot.

7 · Common mix-ups

MythBrighter light gives each electron more energy.

ActuallyBrighter light means more photons, not bigger ones. Only the colour changes each photon's energy.

MythQuantum effects only matter in labs.

ActuallyYour phone's chips and screen only work because of them.

MythPlanck believed in photons.

ActuallyHe saw energy lumps as a maths trick at first. Einstein made them real.

8 · References

CODATA value: Planck constant, NIST, 2018
The International System of Units (SI Brochure, 9th edition), BIPM, 2019
A direct photoelectric determination of Planck's h, R. A. Millikan, Physical Review 7, 1916
Kilogram, Kibble balance, NIST, 2019

Next constantThe elementary charge: Is electric charge smooth, or does it come in lumps?