IB Physics HLTopic 5 — Quantum PhysicsPaper 1 & 2hf = Φ + Ek max~18 min read
The Photoelectric Effect
Shine the right light on a metal and it fires electrons out of its surface. That’s the photoelectric effect — and it’s one of the most important experiments in all of physics, because the old wave picture of light simply cannot explain it. To make sense of what actually happens, Einstein pictured light not as a smooth wave but as a stream of tiny energy packets called photons. One photon in, one electron out. That single idea kicked off the whole of quantum physics — and it’s the story of this page.
📘 What you need to know
The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation shines on it; the emitted electrons are called photoelectrons
Below a certain threshold frequencyf0, no electrons are emitted — no matter how bright the light is
The work functionΦ is the minimum energy needed to free an electron from the surface
The photoelectric equation: hf = Φ + Ek max
Maximum kinetic energy: Ek max = hf − Φ
Max KE depends only on the light’s frequency, never on its intensity (brightness)
Brighter light of the same frequency → more photoelectrons per second, but the same max KE
A graph of Ek max against f is a straight line: gradient = h, y-intercept = −Φ, x-intercept = f0
The stopping potentialVs just halts the fastest electrons: Ek max = eVs
What the experiment shows
Take a clean metal plate and shine light on it. If the light has a high enough frequency, electrons pop straight out of the surface. Here’s the key picture: one photon of light hands all its energy to one electron. It’s a one-to-one deal, like a single ball knocking out a single skittle.
Photons strike the metal. Each electron can absorb only one photon — if that single photon carries enough energy, the electron escapes.
Now here’s the part that broke the old wave theory. If you use light below a certain frequency, nothing happens — not a single electron comes out, even if you crank the brightness up to blinding levels. But go above that special frequency and electrons fly out instantly, even with dim light.
Wave theory said light delivers energy smoothly, like filling a bucket — so any colour of light should eventually free an electron if you wait long enough or make it bright enough. But that’s not what happens. Dim blue light works; blazing red light doesn’t. That only makes sense if light comes in packets and each electron grabs exactly one. A red packet is too small to do the job; a blue packet is big enough. Brightness just means more packets, not bigger ones.
Threshold frequency & work function
Every metal holds onto its surface electrons with a certain “stickiness.” To free one, a photon must deliver at least a minimum amount of energy. That minimum is the work functionΦ.
Work function & threshold frequencyΦ = hf0Φ = work function (J) • f0 = threshold frequency (Hz) • h = Planck’s constant
The threshold frequencyf0 is the smallest frequency of light that will just barely free an electron. A photon exactly at f0 carries just enough energy to release an electron with zero energy left over to spare.
Think of the electron sitting at the bottom of a well, and the work function is the depth of that well. A photon has to supply at least that much energy to lift the electron up and out. Too little energy, and the electron just can’t climb out — it stays put. Different metals have different well depths, which is why they each have their own threshold frequency.
The photoelectric equation
So what happens when a photon has more than the minimum energy? Some of its energy pays the “escape fee” (the work function), and whatever is left over becomes the electron’s kinetic energy — its speed. Energy is just being shared out:
Einstein’s photoelectric equationhf = Φ + Ek maxrearranged: Ek max = hf − Φ
Read it as a simple energy budget: photon energy in = escape fee + leftover speed energy. That’s the whole idea in one line.
hf photon energy in
pays for
Φ escape fee
leftover becomes
Ek max electron speed
Why “maximum” kinetic energy? Because electrons deeper in the metal have to use up extra energy just reaching the surface. The electrons right at the surface lose the least, so they come out fastest — those set the maximum.
WE 1
Zinc has a work function of 4.23 eV. Ultraviolet light of wavelength 250 nm shines on a zinc plate. (a) Show that photoelectrons are emitted. (b) Calculate the maximum kinetic energy of an emitted photoelectron, in eV. (h = 6.63 × 10−34 J s, c = 3.00 × 108 m s−1, 1 eV = 1.60 × 10−19 J)
(a) Step 1 — energy of one photonE = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁴) / (250 × 10⁻⁹)E = 7.96 × 10⁻¹⁹ J = 4.97 eV
Since 4.97 eV > 4.23 eV, the photon beats the work function, so electrons ARE emitted.
(b) Step 2 — photoelectric equationEₖ ₕₓₓ = hf − Φ = 4.97 − 4.23Eₖ ₕₓₓ = 0.75 eVThe trick in part (a): compare photon energy to the work function. Bigger photon → electrons escape. Working in eV keeps the numbers tidy — just subtract. If you want joules, multiply by 1.60 × 10⁻¹⁹.
Intensity vs frequency — the big idea
This is the concept examiners love, because it’s the exact opposite of what the wave model predicts. Turning up the brightness (intensity) does not make electrons come out faster. It only makes more of them come out. Speed is controlled by frequency alone.
You change…
Effect on max KE (speed)
Effect on number of electrons
Higher frequency (bluer light)
Increases — each photon packs more energy
No direct change
Higher intensity (brighter, same colour)
No change — each photon is the same size
Increases — more photons per second
Here’s the analogy that makes it stick. Imagine throwing balls at coconuts. A high-frequency photon is like a heavy cricket ball — one throw and the coconut is gone. A low-frequency photon is a ping-pong ball; throw a thousand and the coconut doesn’t budge. “Brighter light” just means more balls thrown per second — but if each ball is a ping-pong ball, more of them still won’t knock the coconut off. Size of each ball = frequency. Number of balls = intensity.
WE 2
Light of frequency 6.0 × 1014 Hz is shone on a sodium surface with work function 2.28 eV. (a) Calculate the maximum kinetic energy of the photoelectrons, in joules. (b) Calculate the maximum speed of an emitted electron. (h = 6.63 × 10−34 J s, me = 9.11 × 10−31 kg, 1 eV = 1.60 × 10−19 J)
(a) Step 1 — photon energy & work function in jouleshf = (6.63 × 10⁻³⁴)(6.0 × 10¹⁴) = 3.98 × 10⁻¹⁹ JΦ = 2.28 × (1.60 × 10⁻¹⁹) = 3.65 × 10⁻¹⁹ JStep 2 — photoelectric equationEₖ ₕₓₓ = hf − Φ = 3.98 − 3.65 = 3.3 × 10⁻²⁰ JEₖ ₕₓₓ = 3.3 × 10⁻²⁰ J(b) Step 3 — get the speed from ½mv²v = √(2Eₖₕₓₓ/m) = √(2 × 3.3 × 10⁻²⁰ / 9.11 × 10⁻³¹)v = 2.7 × 10⁵ m s⁻¹Convert Φ to joules BEFORE subtracting — mixing eV and J is the classic slip here. Then the fastest electron carries all of Eₖₕₓₓ as ½mv², so rearrange for v.
The straight-line graph
Rearranging the photoelectric equation as Ek max = hf − Φ matches y = mx + c. So a plot of maximum kinetic energy against frequency is a straight line — and it hands you three quantities at once.
The gradient is Planck’s constanth, the x-intercept is the threshold frequencyf0, and extending the line back to the y-axis gives −Φ (the work function). No electrons are emitted below f0.
WE 3
In a photoelectric experiment, a metal of work function 2.0 eV is illuminated with light of wavelength 350 nm. Calculate the stopping potential Vs needed to bring the fastest photoelectrons to rest. (h = 6.63 × 10−34 J s, c = 3.00 × 108 m s−1, 1 eV = 1.60 × 10−19 J)
Step 1 — photon energy in eVE = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁴) / (350 × 10⁻⁹)E = 5.68 × 10⁻¹⁹ J = 3.55 eVStep 2 — maximum kinetic energyEₖ ₕₓₓ = hf − Φ = 3.55 − 2.0 = 1.55 eVStep 3 — stopping potential from Eₖₕₓₓ = eVₛVₛ = Eₖₕₓₓ / e = 1.55 eV / eVₛ = 1.55 VNeat shortcut: when Eₖₕₓₓ is in electronvolts, the stopping potential in volts is just the SAME number, because Eₖₕₓₓ = eVₛ. So 1.55 eV → 1.55 V. The stopping potential is really a direct measure of the maximum kinetic energy.
Stopping potential
How do we actually measure the max KE? We push back against the escaping electrons with a voltage. Turn up a reverse voltage until even the fastest electron is stopped dead just before reaching the far plate. That exact voltage is the stopping potentialVs, and it links straight to the max KE:
Stopping potentialEk max = eVse = elementary charge (1.60 × 10−19 C) • Vs = stopping potential (V)
⚛ Working a photoelectric question
Photon energy?E = hf or E = hc/λ. Pick whichever the question gives you.
Will electrons escape? Compare photon energy to the work function Φ. Only if E > Φ.
Max KE?Ek max = hf − Φ. Keep everything in the same units (all eV or all J).
Max speed? Put Ek max = ½mv2 and solve for v.
Stopping potential?Vs = Ek max/e (in eV, it’s the same number as the volts).
Always check Ephoton vs Φ first — below threshold, nothing happens.
Keep all energies in the same unit (all eV or all J) before subtracting.
Max KE depends on frequency only — never on brightness.
Brighter light of the same colour → more electrons, same speed.
On the graph: gradient = h, x-intercept = f0, y-intercept = −Φ.
In eV, the stopping potential (volts) equals the max KE (eV) numerically.
⚠ Common mistakes
Thinking brighter light gives faster electrons — it gives more, not faster
Mixing eV and joules in the same equation
Forgetting to convert nm to metres (350 nm = 350 × 10−9 m)
Believing low-frequency light works if it’s bright enough — it never does
Reading the y-intercept as +Φ instead of −Φ
Using E = hf with a wavelength — switch to E = hc/λ
Quick recap: The photoelectric effect is electrons being knocked out of a metal by light, and it only works above a threshold frequencyf0. Einstein’s equation hf = Φ + Ek max is an energy budget: photon energy pays the work function escape fee, and the leftover is the electron’s kinetic energy. Max KE depends on frequency alone — brightness only changes how many electrons come out. A graph of Ek max vs f gives h as the gradient, f0 as the x-intercept, and −Φ as the y-intercept, and the stopping potential obeys Ek max = eVs.
The photoelectric effect proved light behaves as particles — a genuinely shocking idea when light was “obviously” a wave. But the story runs deeper. If light waves can act like particles, can particle-things like electrons act like waves? That astonishing question is answered next by Louis de Broglie, who gave every moving particle a wavelength. Next page: The de Broglie Wavelength.
Photoelectric effect not clicking?
Book a free meeting and we’ll drill hf = Φ + Ek max, the intensity-vs-frequency idea, and the straight-line graph.
