Physics · Modern Physics

Photoelectric Effect

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Wrap-up

What you learned

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Read next: Atomic SpectraCarry photon energy into discrete line spectra.

Key takeaway

Threshold frequency decides whether emission can begin at all.
Intensity changes photon flux and current, not the energy carried by each photon.
Above threshold, extra photon energy becomes maximum electron kinetic energy.
Stopping potential measures that maximum kinetic energy by just preventing collection.

Common misconception

Do not treat brightness as stored-up energy that eventually ejects electrons below threshold. In this model, each emitted electron needs one photon above the work-function barrier.

In this bounded model, each emitted electron still needs one photon with enough energy to clear the work-function barrier.

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Discrete line spectraModern Physics

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Stopping-voltage linkElectricity

Electric Potential

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Equation snapshotThreshold and energy snapshot · Maximum emitted-electron energyShow 3 equations

Compare hf with the work function first; only above threshold do current and stopping voltage become meaningful measurements.

Threshold and energy snapshot
$E_{γ} = h f$
Increasing frequency increases the energy carried by each photon.
Maximum emitted-electron energy
$K_{m a x} = h f - ϕ$
After the electron escapes, any extra photon energy becomes maximum kinetic energy.
Stopping potential
$e V_{stop} = K_{m a x}$
The voltage that just stops the fastest electrons measures their maximum kinetic energy.

Why it behaves this way

Explanation

This page asks a simple question: what decides whether light can eject electrons from a metal? The key result is that frequency sets the energy of each photon. If that energy is below the metal's work function, no electrons are emitted, even if you make the beam brighter.

Once the light is above threshold, intensity mainly changes how many electrons are emitted, while frequency changes how energetic the fastest electrons are. The lamp, metal plate, collector plate, readouts, and graphs all stay tied to that same cause-and-effect story.

Key ideas

01Below the threshold frequency, increasing intensity still gives no emitted electrons because each photon is still individually below the work function.

02Above threshold, increasing frequency increases the maximum kinetic energy of emitted electrons, while increasing intensity mainly increases the current.

03The threshold frequency is set by the work function through f_0 = phi / h.

04A negative collector voltage can stop even emitted electrons, and the stopping potential measures the maximum kinetic energy.

Worked examples

Live photoelectric checks

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current frequency 0.38 PHz and work function 2.3 eV, is the light above threshold, and how much energy is left for emitted electrons?

f

Light frequency

0.38 PHz PHz

λ

Wavelength

788.93 nm nm

ϕ

Work function

2.3 eV eV

1. Find the photon energy

With

f = 0.38 P H z

, the photon energy is

h f = 1.57 e V

2. Compare with the threshold

The metal needs

ϕ = 2.3 e V

, so the current threshold is

f_{0} = 0.56 P H z

3. Read the remaining electron energy

That leaves

K_{m a x} = h f - ϕ = 0 e V

, so the live bench says no emission occurs.

Current emission state

h f = 1.57 e V, K_{m a x} = 0 e V, n oe mi ss i o n occ u r s

Because

h f = 1.57 e V

is still below the work function 2.3 eV, the beam remains below threshold and no electrons are emitted.

Common misconception

Use this only when you want to pressure-test a mistaken intuition.

If sub-threshold light is bright enough, electrons can gradually build up enough energy to escape.

In this bounded model, each emitted electron still needs one photon with enough energy to clear the work-function barrier.

Brightness increases how many photons hit the metal, but if each photon is still below threshold, the collector current stays zero.

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