← The photon model

Predict photoelectric outcomes

Farid's bench holds one zinc plate and a shelf of lamps: bright and dim, red through ultraviolet. Before any switch flips, the photon model can predict what the plate will do.

Four explanations are now in hand: the threshold, the instant start, the intensity effect, the frequency effect. This capstone runs them together on any change of lamp.

Three questions settle any case: whether electrons eject, how many each second, and their maximum energy.

First the threshold. Above the metal's threshold frequency, electrons eject; below it, nothing ejects, however bright the light and however long it shines.

before: dim ultraviolet lightzinc plateenergy of one ultraviolet photonafter: bright red lightzinc plateenergy of one red photon
The swap to bright red: many more lumps, every one too small, so the plate goes silent.

Then the count. For above-threshold light, more intensity means more photons each second, so more ejections each second.

Then the energy. A higher frequency means a bigger lump per photon, so a higher maximum electron energy. Intensity never moves it.

changeejectejections each secondmaximum electron energyraise the intensityyes, unchangedmoreunchangedraise the frequencyyes, unchangedunchanged at the same count of photonshigherdrop below the thresholdnononenone to report
The capstone grid: each dial answers its own question.

Changes can come two at a time; take them one dial at a time. Frequency answers whether electrons eject and how energetic they are. Intensity answers how many each second.

Farid swaps dim ultraviolet for bright red on zinc. Red sits below zinc's threshold. Prediction: the ejections stop entirely, and all that brightness changes nothing.

Swap back the other way and both answers return at once: ejection resumes instantly, with the maximum energy set by the ultraviolet frequency alone.

before: dim violet lighta second metalafter: bright green lightthe same metal
Both dials moved at once: more ejections each second, each electron with less energy to spare.

On zinc, a dim ultraviolet lamp is replaced by a bright red one. Predict what the plate does.

Ask the threshold question first: red sits below zinc's threshold frequency.

So no red photon can free an electron, and electrons cannot pool lumps.

The brightness dial is useless below threshold: more photons just means more too-small lumps.

Ejection stops entirely. The bright red lamp ejects nothing, however long it shines.

On a metal whose threshold lies in yellow light, a dim violet lamp is replaced by a bright green one. Predict the three answers.

Threshold: green sits above yellow in frequency, so electrons still eject.

Count: the green lamp is brighter, so more photons arrive each second, so more ejections each second.

Energy: green sits below violet in frequency, so each photon is a smaller lump, so the maximum electron energy falls.

Still ejecting; more electrons each second; a lower maximum electron energy.

A lamp above a metal's threshold is made brighter, frequency unchanged. How many electrons leave each second?

A bright lamp below a metal's threshold shines on the plate for an hour. What is the total count of ejected electrons?

Hamish says: 'On a metal whose threshold lies in blue light, a dim violet lamp will eject electrons, just a few each second.' Is Hamish correct?

Your turn

On one metal, a dim ultraviolet lamp is replaced by a brighter lamp of lower frequency that is still above the threshold. Which pair of changes follows?

A plate ejects nothing under a red lamp. The lamp is made ten times brighter. What happens?

A swap of lamps on one plate raises the maximum energy of the ejected electrons. Which property of the light must have risen?