What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

Define work function of a metal.

The minimum energy required to liberate an electron from the metal's surface.

Why does intensity not affect the energy of photoelectrons?

Each electron absorbs one photon; energy depends on photon frequency, while intensity sets photon number.

Write Einstein's photoelectric equation.

\(K_{max}=h\nu-\phi_0\), relating maximum kinetic energy to frequency and work function.

What is the threshold frequency?

The minimum frequency \(\nu_0=\phi_0/h\) below which no electrons are emitted however intense the light.

What is stopping potential?

The minimum reverse potential \(V_0\) that stops the fastest photoelectrons; \(eV_0=K_{max}\).

How does stopping potential depend on intensity?

It is independent of intensity; it depends only on the frequency of incident light.

State de Broglie's hypothesis.

A moving particle has an associated wavelength \(\lambda=h/p=h/mv\).

Which experiment confirmed the wave nature of electrons?

The Davisson-Germer experiment, showing electron diffraction by a crystal.

Why is the wave nature of macroscopic objects not observed?

Their large momentum gives an extremely small wavelength, far too tiny to detect.

What evidence shows the particle nature of light?

The photoelectric effect, explained only by quantised photons of energy \(h\nu\).

Dual Nature of Radiation and Matter

Class 12 Physics · Physics Part II · Chapter 3

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Summary

Experiments on electron emission and the photoelectric effect revealed that radiation has a particle character, while matter shows wave behaviour—together establishing wave-particle duality. Electrons can be freed from a metal by heat, light, strong fields or collisions, the minimum energy needed being the work function \(\phi_0\). In the photoelectric effect, light above a threshold frequency ejects electrons instantly, the maximum kinetic energy depending on frequency, not intensity—facts classical wave theory cannot explain. Einstein resolved this with the photon idea: light is quantised into packets of energy \(E=h\nu\), and his photoelectric equation \(K_{max}=h\nu-\phi_0\) accounts for the threshold, the linear frequency dependence and the instantaneous emission. Intensity sets the number of photons, hence the current, while frequency sets each photon's energy. Conversely, de Broglie proposed that particles have an associated wavelength \(\lambda=\dfrac{h}{p}=\dfrac{h}{mv}\), confirmed by the Davisson-Germer experiment in which electrons diffract like waves. Thus radiation and matter each display both wave and particle aspects, a cornerstone of quantum physics.

Electron emission and work functionPhotoelectric effect and its lawsEinstein's photoelectric equationPhoton picture of lightde Broglie wavesDavisson-Germer experiment

Key terms

Work function

Minimum energy \(\phi_0\) needed to eject an electron from a metal surface.

Photoelectric effect

Emission of electrons from a metal when light above the threshold frequency falls on it.

Photon

Quantum of light energy \(E=h\nu\), behaving as a particle.

Threshold frequency

Minimum frequency below which no photoemission occurs.

de Broglie wavelength

Wavelength of a moving particle, \(\lambda=h/p\).

Stopping potential

Reverse voltage that just stops the most energetic photoelectrons.

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The work function of a metal is the:

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