Quantum physics · Photoelectric effect

What controls the electrons?

Watch photoelectrons emerge with different speeds, then use an electric field to accelerate, slow or stop them.

By the end, you should be able to explain Frequency sets the maximum energy; emission depth produces a spread of electron speeds.

Investigation 1

Watch photoelectrons leave the metal

Watch: wavelength changes electron energy; intensity changes how many are released.

Live photocell

Light on a metal cathode

Below threshold

A glass vacuum photocell containing a curved cathode on the left and a collector plate on the right.

CathodeSodium

Collectorcollects electrons

650 nmred light

What you observe Photon energy is too low to release electrons.

Photocurrent 0.0 nA

1 Live controls

Change the light

Metal cathode φ = 2.28 eV Wavelength 650 nm

UV · higher fred · lower f

Light intensity 40%

fewer photonsmore photons

Live energy balanceBelow the emission threshold

photon— = work function— + maximum KE—

Threshold wavelength for this metal—

2 Emission depth

Why do electrons leave at different speeds?

Latest photon event Waiting for the first photon…

Near the surface0.00 eV

From deeper inside0.00 eV

Model: electrons excited deeper inside the metal lose more energy in collisions before reaching the surface. The depth is within the metal—not inside the nucleus. Screen speeds use one fixed scale and preserve v ∝ √E_k.

→

Now add an electric field.
Reverse the polarity to accelerate or stop the electrons.

Investigation 2

How energetic are the fastest electrons?

Explore: a positive collector accelerates electrons; a negative collector slows them.

Sodium · 300 nm UV · no electric field

Electric field across the photocell

Current12.7 nA

The same photocell, with the collector negative relative to the cathode so emitted electrons are repelled.

+ −

Your live trace

Photocurrent against collector potential

measured current

1 Choose the field direction

Reverse the polarity

Potential magnitude 0.00 V

0 V3.20 V

Collector potential0.00 V

Photocurrent12.7 nA

Field effectNo change at 0 V

Fastest KE leaving metal1.85 eV

Fastest KE at collector1.85 eV

Speed at collector8.07 × 10⁵ m/s

With no potential difference, the field does no work on the electrons.

2 Measure the stopping potential

Use a negative collector. Find the smallest magnitude that reduces the current to zero.

Adjust the voltage until the current just reaches 0.0 nA.

Frequency setsenergy per photon

So it controls whether electrons are emitted and their maximum kinetic energy.

Intensity setsphoton arrival rate

Above threshold, this changes the photocurrent but not the stopping potential.

Stopping potential measuresmaximum electron KE

The fastest electrons are stopped when eV_s = E_k(max).

Extension How can stopping potential give Planck's constant?Use several frequencies and plot V_s against f

From Einstein's equation

V_s = he f − φe

A straight-line graph of stopping potential against frequency has gradient h/e.

Repeat the stopping-potential measurement for several frequencies.
Plot V_s on the vertical axis and f on the horizontal axis.
Multiply the gradient by e to estimate Planck's constant.