Photoelectric Effect — Einstein's Photons Explained

Q: What is the photoelectric effect?

When light above a threshold frequency strikes a metal, electrons are ejected instantly. Brighter light ejects more electrons (more current) but each electron's energy depends only on the light's frequency — inexplicable for waves, obvious for photons.

Q: What is Einstein's photon equation?

E = hf: each photon carries energy proportional to its frequency (h = 6.626×10⁻³⁴ J·s). Part of it pays the metal's work function φ (the electron's escape cost); the remainder becomes the electron's kinetic energy.

Q: Why does brighter light not make faster electrons?

Increasing brightness sends more photons per second, so more electrons are ejected per second — higher current. But each photon still carries the same hf, so no single electron gets more energetic.

Q: What is the threshold frequency?

Below the threshold frequency f₀ = φ/h, single photons lack the energy to free any electron — no matter how bright the light or how long you wait. This sharp cutoff was the wave theory's death blow.

Introductory College⏱ 10 min readModern Physics

The photoelectric effect: Einstein's photon explanation, E = hf = φ + KE_max, threshold frequency, and why it proved light is quantized.

Quick answer

The photoelectric effect is the ejection of electrons from a metal by light — but only if the light's frequency exceeds a threshold. Einstein explained it in 1905: light arrives as photons, each carrying E = hf; one photon frees one electron.

$hf = \phi + KE_{max}$

Unit: Energies in joules or eV; f in Hz

Example: Ultraviolet light on sodium ejects electrons instantly, even when dim. Bright red light — carrying more total power — ejects none, because each red photon is below the threshold energy. Frequency, not brightness, decides.

What you will learn

Describe the photoelectric effect observations
State Einstein's photon hypothesis E = hf
Apply hf = φ + KE_max to threshold problems
Explain why brightness affects current but not electron energy
Connect the effect to solar cells and sensors

The experiment that broke wave theory

In 1887 Heinrich Hertz noticed something odd: ultraviolet light helped sparks jump between metal electrodes. By 1902 Philipp Lenard had mapped the puzzle precisely — and wave theory could not solve it:

Brighter light ejected more electrons, but not faster ones.
Below a threshold frequency, no electrons emerged — however bright, however long.
Emission was instantaneous, with no energy build-up time.

Waves should do the opposite: brighter waves carry more energy per electron, and dim light should work if you wait. In 1905, a 26-year-old patent clerk named Albert Einstein proposed the radical fix.

Einstein’s photon hypothesis

Einstein suggested light itself comes in quanta — photons — each carrying energy proportional to frequency:

hf = \phi + KE_{max}

h = Planck's constant (6.626×10⁻³⁴ J·s), φ = work function of the metal, KE_max = fastest electrons' kinetic energy

One photon, one electron

A photon gives all its energy to a single electron or none at all. This all-or-nothing exchange is why brightness (photon count) and electron energy (photon energy) are independent.

Paying the work function

The work function φ is the metal's electron escape fee — typically a few electronvolts. A photon with $hf > \phi$ pays the fee and the electron keeps the change as kinetic energy; a photon with $hf < \phi$ is turned away entirely.

Worked example. Sodium's work function is 2.75 eV. Light of frequency $7.0 \times 10^{14}$ Hz strikes it. Max electron energy?

$E_{photon} = hf = (4.136 \times 10^{-15}\ \mathrm{eV·s})(7.0 \times 10^{14}\ \mathrm{Hz}) = 2.90\ \mathrm{eV}$

$KE_{max} = 2.90 - 2.75 = 0.15\ \mathrm{eV}$

Barely ejected — the light is just above sodium's threshold. Drop the frequency slightly and emission stops dead.

One photon in, one electron out — if hf clears the work function φ. The leftover energy becomes the electron's speed.

From sparks to solar panels

Millikan spent a decade trying to disprove Einstein — and confirmed him instead, measuring h precisely from photoelectric data. The photon was real, and light's wave-particle duality was born.

The effect now works for civilization: solar panels are giant photoelectric devices (photons freeing charges across silicon junctions), camera sensors count photoelectrons, and automatic doors watch for interrupted beams. A 1905 puzzle about sparks became the physics of clean energy.

Variables and units

Symbol	Name	Unit	Meaning
$E$	Photon energy	J or eV	Energy of one photon
$h$	Planck constant	J·s	Planck's constant
$f$	Frequency	Hz	Light frequency
$φ$	Work function	J or eV	Minimum energy to free an electron from the metal
$KE_max$	Max kinetic energy	J or eV	Kinetic energy of the fastest ejected electrons

Common mistakes

✗ Einstein won the Nobel Prize for relativity.

His 1921 Nobel Prize was specifically 'for his discovery of the law of the photoelectric effect.' Relativity was still controversial; the photon was experimentally undeniable.

✗ Brighter light always means more energetic electrons.

Brightness controls the number of photons (current); frequency controls each photon's energy (electron speed). A dim blue beam beats a blinding red floodlight at ejecting fast electrons.

✗ There is a delay while electrons 'soak up' wave energy.

Emission is instantaneous — even at the dimmest intensities. Waves would need time to accumulate energy; photons deliver it in one quantum punch. This immediacy was decisive evidence.

Real-world applications

Solar panels: photovoltaic cells are photoelectric devices — photons knock electrons loose to drive current.
Digital cameras: CCD and CMOS sensors count photoelectrons to build images pixel by pixel.
Night vision: photocathodes convert scarce photons into electrons, amplified into visible images.
Automatic doors and light meters: photoelectric sensors detect beams of light being interrupted.

Frequently asked questions

What is the photoelectric effect?

When light above a threshold frequency strikes a metal, electrons are ejected instantly. Brighter light ejects more electrons (more current) but each electron's energy depends only on the light's frequency — inexplicable for waves, obvious for photons.

What is Einstein's photon equation?

E = hf: each photon carries energy proportional to its frequency (h = 6.626×10⁻³⁴ J·s). Part of it pays the metal's work function φ (the electron's escape cost); the remainder becomes the electron's kinetic energy.

Why does brighter light not make faster electrons?

Increasing brightness sends more photons per second, so more electrons are ejected per second — higher current. But each photon still carries the same hf, so no single electron gets more energetic.

What is the threshold frequency?

Below the threshold frequency f₀ = φ/h, single photons lack the energy to free any electron — no matter how bright the light or how long you wait. This sharp cutoff was the wave theory's death blow.