Photons and the photoelectric effect

By the end you’ll be able to

Use E = hf = hc/λ and convert between joules and electronvolts

Apply Einstein’s photoelectric equation hf = φ + Ek(max) and interpret graphs of Ek(max) against f

Explain threshold frequency and instantaneous emission as evidence against the wave model

Describe stopping potential measurements and the effect of intensity versus frequency on photocurrent

Estimate photon numbers from power and wavelength

What the exam asks

Photon energy in joules and eV, and photons emitted per second by a source of given power.

Einstein’s equation

hf = \phi + E_{k(\max)}

, with threshold frequency (or wavelength) and work function.

Graphs of

or against : from the gradient, and from the intercepts, parallel lines for different metals.

Board differences

AQA (3.2.2.1): the data booklet gives $E = hf = hc/\lambda$ and $hf = \phi + E_{k(\max)}$ . Stopping potential is on the specification, but you need not describe the apparatus.
Edexcel 9PH0 and IAL: $E = hf$ and $hf = \phi + \tfrac{1}{2}mv^2_{\max}$ are on the data sheet. Know threshold frequency, the electronvolt, and how the effect gives evidence for the particle nature of light.
OCR A (4.5.1–4.5.2): the electroscope demonstration, the one-to-one photon–electron interaction, and the LED determination of $h$ (a PAG practical).
OCR B: the photon model, $E = hf$ , the LED method for $h$ , and the photoelectric effect as evidence for quanta.
Cambridge 9702 (22.1–22.2): you must recall $E = hf$ and $hf = \Phi + \tfrac{1}{2}mv^2_{\max}$ , because they are not on the formulae page. You also need threshold wavelength and photon momentum .
Eduqas, WJEC and CCEA: the vacuum photocell, stopping-potential measurements, and graphs of $E_{k\max}$ against $f$ .

Core ideas

Photons and the electronvolt

Electromagnetic radiation is emitted and absorbed in discrete packets of energy (quanta) called photons. The energy of one photon is

E = hf = \frac{hc}{\lambda}, \qquad h = 6.63 \times 10^{-34}\ \text{J s}

The electronvolt is the energy transferred when one electron moves through a potential difference of 1 V:

1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}

To convert joules to eV, divide by $1.60 \times 10^{-19}$ . Visible photons carry roughly 1.8 eV (700 nm, red) to 3.1 eV (400 nm, violet). A useful check is $E(\text{eV}) \approx 1240/\lambda(\text{nm})$ , but always show the full method in the exam.

For a monochromatic beam of power $P$ , the number of photons per second is

\frac{N}{t} = \frac{P}{hf} = \frac{P\lambda}{hc}

A photon also carries momentum $p = E/c = h/\lambda$ . Cambridge requires this, and it links to the de Broglie equation in the next topic.

The photoelectric effect: what is observed

When electromagnetic radiation of high enough frequency falls on a clean metal surface, electrons called photoelectrons are emitted.

Electrons are emitted only if the frequency is at or above a threshold frequency $f_0$ , which depends on the metal. Below $f_0$ nothing is emitted, however intense the radiation.
Above $f_0$ , emission starts , even at very low intensity.

The photon explanation

Each photon interacts with one electron and gives it all its energy $hf$ .
To escape, an electron must do work against the attraction of the metal. The work function $\phi$ is the minimum energy needed to remove an electron from the surface.
An electron at the surface escapes with the most energy. Electrons deeper in the metal lose energy in collisions on the way out, which is why there is a range of energies up to a maximum.

hf = \phi + E_{k(\max)}

Threshold: $hf_0 = \phi$ , so $f_0 = \phi/h$ and the threshold wavelength is .

Observation	Wave model predicts	Photon model explains
Threshold frequency	Any frequency should release electrons if the light is intense enough, or if you wait long enough	One photon with $hf < \phi$ cannot release an electron, however many photons arrive
Instant emission	At low intensity, electrons need time to absorb enough energy	One photon delivers all its energy at once
$E_{k(\max)}$ independent of intensity

Stopping potential and the photocell

In a vacuum photocell, light falls on a curved metal cathode. Photoelectrons cross to the anode, and a microammeter records the current. If the anode is made negative relative to the cathode, it repels the electrons. The current falls to zero at the stopping potential $V_s$ , when even the fastest electrons are turned back:

eV_s = E_{k(\max)} \quad\Rightarrow\quad V_s = \frac{h}{e}f - \frac{\phi}{e}

On a graph of current against anode p.d., the current levels off (saturates) at positive p.d.s, when every emitted electron is collected. The saturation current is proportional to intensity. The stopping potential depends only on the frequency and the metal.

Reading the graphs

Graph	Gradient	$x$ -intercept	$y$ -intercept (extrapolated)
$E_{k(\max)}$ against

Different metals give parallel lines, because the gradient is always $h$ (or $h/e$ ). A metal with a larger work function gives a line shifted to the right, with a larger $f_0$ .

Zinc plate and electroscope (OCR A)

A negatively charged zinc plate sits on a gold-leaf electroscope. Ultraviolet light makes the leaf fall, because electrons are emitted and the plate loses its charge. Bright visible light does nothing, because each photon has too little energy. If the plate is positively charged, the leaf stays up under ultraviolet light, because the emitted electrons are attracted back to the plate.

Finding $h$ with LEDs (OCR A, OCR B)

An LED starts to emit light when the p.d. across it reaches a threshold value $V_0$ . At that point, the energy $eV_0$ given to each electron is roughly the energy of one photon, $hc/\lambda$ . Plot against for LEDs of several colours. The gradient is , so .

Worked examples

Exam technique

The 6-mark “evidence” question has three strands: the observations, the photon explanation, and why the wave model fails. Give each strand specific physics.
Write “one photon is absorbed by one electron”. Examiners look for this one-to-one idea.
“Show that” with eV: write the $1.60 \times 10^{-19}$ conversion out explicitly.
Graphs: use a gradient triangle covering more than half the line, read intercepts only after extending it, and include the power of ten from an axis labelled “ $f$ / $10^{14}$ Hz”.

Common mistakes

Quick recap

$E = hf = hc/\lambda$ , and $1\ \text{eV} = 1.60 \times 10^{-19}$ J.

By the end you’ll be able to

What the exam asks

Check your understanding

Flashcards

Core ideas

Photons and the electronvolt

The photoelectric effect: what is observed

The photon explanation

Stopping potential and the photocell

Reading the graphs

Zinc plate and electroscope (OCR A)

Finding $h$ with LEDs (OCR A, OCR B)

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

vii.Check your understanding

viii.Flashcards

Core ideas

Photons and the electronvolt

The photoelectric effect: what is observed

The photon explanation

Stopping potential and the photocell

Reading the graphs

Zinc plate and electroscope (OCR A)

Finding hhh with LEDs (OCR A, OCR B)

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards

Finding $h$ with LEDs (OCR A, OCR B)