Dual Nature of Radiation and Matter

part 1

Photoelectric Effect

• Electron emission — types
• Photoelectric effect — Hertz and Lenard's observations
• Experimental setup for photoelectric effect
• Effect of intensity and frequency on photoelectric current

part 2

Einstein's Theory

• Einstein's photoelectric equation
• Photon and its properties
• Stopping potential and work function
• Particle nature of light — photon

part 3

Wave Nature of Matter

• de Broglie hypothesis
• de Broglie wavelength
• Davisson and Germer experiment
• Heisenberg uncertainty principle (qualitative)

Photon energy

$E = hf = \frac{hc}{\lambda}$

★ board favourite

Einstein's photoelectric equation

$KE_{max} = hf - \phi = h(f - f_0)$

★ board favourite

de Broglie wavelength

$\lambda = \frac{h}{mv} = \frac{h}{p}$

★ board favourite

de Broglie λ for accelerated electron

$\lambda = \frac{h}{\sqrt{2meV}}$

★ board favourite

Photon momentum

$p = \frac{h}{\lambda} = \frac{E}{c}$

★ frequently asked

Work function

$\phi = hf_0$ (f₀ = threshold frequency)

★ frequently asked

Stopping potential

$eV_0 = KE_{max}$

★ frequently asked

de Broglie λ in terms of KE

$\lambda = \frac{h}{\sqrt{2m\cdot KE}}$

★ frequently asked

State the laws of the photoelectric effect. Using Einstein's photoelectric equation, explain the effect of (i) intensity and (ii) frequency of incident radiation on the photoelectric current and the stopping potential. Draw the relevant graphs.

Derive an expression for the de Broglie wavelength of an electron accelerated through a potential difference of V volts.

State Einstein's photoelectric equation. Explain the terms work function and stopping potential. A photon of energy 5eV falls on a metal with work function 3eV. Find the maximum kinetic energy and stopping potential.

An electron and a proton have the same kinetic energy. Which has the longer de Broglie wavelength? Justify.

Define work function of a metal. How does the maximum kinetic energy of photoelectrons vary with the frequency of incident radiation? Draw the graph.

The threshold frequency of a metal is 4×10¹⁴ Hz. Light of frequency 8×10¹⁴ Hz is incident on it. Calculate (i) the work function, (ii) the maximum kinetic energy of the emitted electrons, and (iii) the stopping potential. (h = 6.6×10⁻³⁴ J·s)

Why does the photoelectric emission not take place below a certain threshold frequency, no matter how intense the incident light is?

Calculate the energy and momentum of a photon of light of wavelength 500 nm. (h = 6.6×10⁻³⁴ J·s, c = 3×10⁸ m/s)

How many marks is Dual Nature of Radiation and Matter worth in the Class 12 board exam?

Around 4 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. Einstein's photoelectric equation — practise threshold frequency numerics.

Is Dual Nature of Radiation and Matter easy or hard?

It's rated medium — a moderate-difficulty chapter in Class 12 Physics. Most students need about 3 hours to cover it well.

What are the important topics in Dual Nature of Radiation and Matter?

The chapter covers 10 NCERT topics in 3 areas: Photoelectric Effect; Einstein's Theory; Wave Nature of Matter.

What questions come from Dual Nature of Radiation and Matter in board exams?

Between 2019–2024, CBSE board papers asked questions from this chapter on Photoelectric Effect, de Broglie Wavelength, de Broglie, Work Function — 1- to 5-mark questions.