Photoelectric Effect

Dual Nature of Radiation and Matter · CBSE

Theory

The statement of the phenomenon, the historical observations of Hertz, Hallwachs and Lenard, and the definitions of threshold frequency and of intensity in the photon picture. CBSE sets these as one-mark definitions and as the opening part of longer answers.

Photoelectric effect: the phenomenon of emission of electrons from a metal surface when light of suitable frequency is incident on it. The emitted electrons are called photoelectrons, and the substances that show the effect are called photosensitive substances.
It converts light energy into electrical energy, and it obeys the law of conservation of energy — that conservation statement is exactly what Einstein's equation expresses.

While producing electromagnetic waves by spark discharge, Heinrich Hertz noticed that the high-voltage sparks across his detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.
Interpretation: light falling on the metal surface helped free charged particles — electrons, as we now know — to escape. Electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions and leave the surface.

Hallwachs connected a negatively charged zinc plate to an electroscope and shone ultraviolet light on it.

Initial state of the zinc plate	Effect of ultraviolet light
Negatively charged	the plate lost its charge
Uncharged	the plate became positively charged
Positively charged	the positive charge was further enhanced

All three results point the same way: negatively charged particles are being emitted from the plate under the action of ultraviolet light.

Lenard used an evacuated glass tube with two metal electrodes. Ultraviolet radiation on the emitter plate C caused a current to flow in the external circuit; when the radiation was stopped, the current stopped at once.
Interpretation: UV light ejects electrons from C; the electric field of the battery drives them to the positive collector plate A; their flow through the evacuated tube is the current.
Hallwachs and Lenard together studied how the photocurrent varies with collector plate potential, with frequency and with intensity — the systematic study taken up in the next section.
They also found that no electrons at all are emitted when the frequency of the incident light is below a certain minimum value, which depends on the material of the emitter plate.

Definition to write verbatim: threshold frequency is the minimum frequency of the incident radiation below which photoelectric emission does not occur, however large the intensity of light may be.
It is different for different metals, being fixed by the work function: $\nu_0 = \phi_0/h$ .
Equivalently there is a threshold wavelength $\lambda_0 = c/\nu_0 = hc/\phi_0$ , and emission requires $\lambda \le \lambda_0$ .

Zinc, cadmium and magnesium respond only to ultraviolet light — short wavelength, high photon energy — because their work functions are relatively large.
The alkali metals lithium, sodium, potassium, caesium and rubidium have small work functions and are photosensitive even to visible light.
Different photosensitive materials respond differently: selenium is more sensitive than zinc or copper. The same material responds differently to different wavelengths — ultraviolet light causes emission from copper, while green or red light does not.
Exam-ready examples: for emission with ultraviolet light, name zinc or cadmium; for emission with visible light, name lithium or sodium.

Definition: the intensity of electromagnetic radiation is the amount of light energy — that is, the number of photons multiplied by the energy of each photon — incident per unit area per unit time.

$I = \dfrac{n\,h\nu}{A\,t}$

$n$ = number of photons incident normally on area $A$ in time $t$ . SI unit W m $^{-2}$ , equivalently J m $^{-2}$ s $^{-1}$ .
In the wave picture, intensity is set by the square of the amplitude of the wave. In the photon picture, at a given frequency, it is set purely by the number of photons arriving per unit area per unit time — each photon still carries the same energy $h\nu$ .

Emission occurs only if $h\nu > \phi_0$ , i.e. $\nu > \nu_0$ , i.e. $\lambda < \lambda_0$ .
Emission is instantaneous once that condition is met: the time lag is $10^{-9}$ s or less, even for very dim light.
Photoelectric effect is the phenomenon to name when asked which phenomenon shows the quantum (particle) nature of electromagnetic radiation.

Real board questions. Answers are at the end of the page.

1
Define the term threshold frequency in photoelectric emission. OR Define the term "threshold frequency", in the context of photoelectric emission.
1 markCBSE Class 12 Physics — Very Short Answer · 2020 / Delhi 2019, R · Section A, 1 markAnswer 1 ↓
2
Define the term "Intensity" in the photon picture of electromagnetic radiation.
1 markCBSE Class 12 Physics — Very Short Answer · Delhi 2019 · Section A, 1 markAnswer 2 ↓

Work the questions above first, then check yourself here. Each answer is set out the way it should be written in the paper.

1.↑ back to the question
Threshold frequency is defined as the minimum frequency of the incident radiation below which photoelectric emission does not occur, however large the intensity of light may be.
2.↑ back to the question
In the photon picture, the intensity of electromagnetic radiation is the amount of light energy (i.e. the number of photons multiplied by the energy of each photon) incident per unit area per unit time.