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The photoelectric effect is the emission of electrons from a metal surface when light shines on it. First observed by Heinrich Hertz in 1887 (ironically, while he was working on experiments that confirmed Maxwell's wave theory of electromagnetism), it was studied carefully by Philipp Lenard in the years that followed. By around 1902, Lenard had established a set of striking experimental facts about the effect — facts which, taken together, were completely incompatible with the classical wave theory of light.
This lesson presents those observations, explains why they were so shocking in 1902, and prepares the way for Einstein's 1905 explanation in terms of photons (Lesson 4).
The photoelectric effect is central to the OCR A-Level Physics A specification (H556), Module 4.5. Understanding it qualitatively — what was observed, and why the wave theory cannot explain it — is just as important as the numerical work which follows.
The classic photoelectric experiment uses a vacuum photocell: a sealed glass tube from which the air has been pumped out, containing two metal electrodes connected to an external circuit.
When light of sufficiently high frequency strikes the cathode, electrons are ejected from the metal surface. These electrons are called photoelectrons (though they are ordinary electrons — the prefix merely records how they were liberated). If the anode is held at a positive potential relative to the cathode, the photoelectrons are attracted to it, and a current flows in the external circuit. This photocurrent can be measured by an ammeter.
flowchart LR
L[Light source] --> C[Cathode]
C -- photoelectrons --> A[Anode]
A --> I[Ammeter]
I --> V[Variable p.d.]
V --> C
By varying (a) the frequency of the incident light, (b) the intensity of the incident light, and (c) the potential difference between the electrodes, Lenard discovered four distinct experimental facts which together constitute the observations of the photoelectric effect.
No photoelectrons are emitted unless the frequency of the incident light is above a certain minimum, called the threshold frequency f₀, regardless of how intense the light is.
If you shine red light (say, 650 nm) on a clean zinc plate for an hour, not a single electron is liberated. But if you switch on a UV lamp, even a very dim one, photoelectrons are emitted immediately. The threshold is sharp: a tiny change in wavelength around the threshold is the difference between no current and a measurable current.
The threshold frequency depends on the metal. For zinc, f₀ ≈ 1.0 × 10¹⁵ Hz (far-UV). For caesium, f₀ ≈ 5 × 10¹⁴ Hz (visible green). For copper, f₀ is deep in the ultraviolet.
On the classical wave picture, light of any frequency delivers energy continuously to the metal. A sufficiently bright red lamp ought, eventually, to pump enough energy into a surface electron for it to escape — the process might take a while, but it should happen. The experimental absence of emission at low frequencies, no matter how bright the light, is completely at odds with this expectation.
When the frequency is above threshold, photoelectrons are emitted immediately — within less than 10⁻⁹ s of the light being switched on — no matter how dim the light.
Even at very low light intensities, there is no detectable delay between illumination and photoemission. The first electron flies off as soon as the first photons arrive.
On the classical wave picture, a very dim light would deposit energy very slowly into the electrons of the metal. For a surface electron to absorb enough energy to escape might take minutes or even hours. The prediction is:
t_delay ≈ E_escape / P_absorbed_per_electron
For a typical work function of 4 eV and a very dim light, this delay can be calculated to be of order seconds to minutes. The observed delay is less than a nanosecond — many orders of magnitude faster than the wave theory allows.
Above the threshold, the number of photoelectrons emitted per second is proportional to the intensity of the light. But the maximum kinetic energy of each photoelectron is independent of intensity.
This was perhaps the most astonishing of Lenard's findings. You can double the brightness, triple it, increase it by a factor of a hundred — and while the photocurrent rises correspondingly, the fastest photoelectrons still come out at exactly the same speed.
To measure the maximum kinetic energy, Lenard used the stopping potential method: he reversed the polarity of the external p.d. and increased it until the photocurrent just fell to zero. At this point, no photoelectron has enough kinetic energy to climb the potential hill between cathode and anode, and the work done against the field equals the maximum initial kinetic energy:
eV_s = KE_max
The stopping potential V_s is a direct measure of KE_max. And this stopping potential is independent of intensity.
On the classical wave picture, a more intense light has a larger amplitude of the electric field. A larger electric field exerts a larger force on each electron, so each electron should oscillate more vigorously and carry away more kinetic energy when it escapes. The observation that KE_max is fixed, no matter the intensity, is simply inexplicable.
The maximum kinetic energy of photoelectrons increases linearly with the frequency of the incident light, and is zero at the threshold frequency f₀.
If you plot KE_max (or equivalently eV_s) against frequency f, you get a straight line:
h (Planck's constant!)f₀ (the threshold frequency)-φ (the negative of the work function)This linear relationship, which holds with astonishing precision, is one of the most striking results in physics. It is the experimental smoking gun for Einstein's photon theory.
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