JEE Advanced 2026 Paper 2 — Full Mock Test (54 Questions, 180 Marks)
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This MCQ module is based on: Particle Nature Light
TOPIC 10 OF 27
Particle Nature Light
🎓 Class 12
Physics
CBSE
Theory
Ch 11 – Dual Nature of Radiation and Matter
⏱ ~14 min
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Particle Nature Light
11.9 The Photon — A Particle of Light
Einstein's quantum hypothesis (1905) was so radical it took twenty years to be widely accepted. By the time Compton's X-ray scattering experiments (1923) had demonstrated photons carrying momentum, the case was essentially closed. The particle of light is now called the photon — a name coined by chemist G. N. Lewis in 1926.
Photon — the quantum of electromagnetic radiation. For radiation of frequency \(\nu\) and wavelength \(\lambda\) in vacuum:
- Energy: \(E = h\nu = \dfrac{hc}{\lambda}\)
- Momentum: \(p = \dfrac{E}{c} = \dfrac{h\nu}{c} = \dfrac{h}{\lambda}\)
- Speed: \(c = 3\times10^{8}\) m/s in vacuum (always).
- Rest mass: zero (a photon at rest does not exist).
- Charge: zero (unaffected by electric and magnetic fields).
Properties of Photons (NCERT summary)
- In radiation of frequency \(\nu\), every photon has the same energy \(E = h\nu\) and momentum \(p = h\nu/c\), regardless of intensity.
- Photons are electrically neutral; they are not deflected by electric or magnetic fields.
- In a photon-particle collision (e.g. photon-electron), total energy and momentum are conserved. However, the number of photons need not be — they can be created or absorbed.
- Even though a photon carries energy and momentum, its rest mass is zero. We can speak only of its "effective" or "relativistic" mass \(m=h\nu/c^2 = h/(\lambda c)\).
- The intensity of light at a given frequency equals the number of photons crossing unit area per unit time, multiplied by \(h\nu\).
11.10 The Energy and Momentum Numbers — Why Photons Matter
Different parts of the electromagnetic spectrum carry vastly different photon energies. The same equation \(E=h\nu\) tells us that a single γ-ray photon packs millions of times more punch than a radio-wave photon:
| Region | Wavelength λ | Frequency ν | Energy hν | Photon character |
|---|---|---|---|---|
| Radio (FM) | 3 m | 10⁸ Hz | 4 × 10⁻⁷ eV | Wave-like in everyday use |
| Microwave | 3 cm | 10¹⁰ Hz | 4 × 10⁻⁵ eV | Heats water; rotates molecules |
| Infrared | 10 μm | 3 × 10¹³ Hz | 0.12 eV | Vibrates molecular bonds |
| Visible (yellow) | 580 nm | 5.2 × 10¹⁴ Hz | 2.14 eV | Photo-emits Cs surface |
| UV | 250 nm | 1.2 × 10¹⁵ Hz | 5.0 eV | Photo-emits most metals |
| X-ray | 0.1 nm | 3 × 10¹⁸ Hz | 12 keV | Crystal diffraction; ionising |
| γ-ray | 10⁻¹² m | 3 × 10²⁰ Hz | 1.2 MeV | Nuclear transitions; particle creation |
Useful number: A handy mnemonic is \(E\,(\text{eV}) = \dfrac{1240}{\lambda\,(\text{nm})}\). So 620 nm light → 2 eV photon; 124 nm UV → 10 eV photon.
11.11 Photon Number — How Many Per Second?
Even modest sources emit staggering numbers of photons. A 1-watt yellow lamp (λ = 580 nm) sends out:
\[N = \frac{P}{h\nu} = \frac{1\,\text{W}}{2.14\,\text{eV}\times1.602\times10^{-19}\,\text{J/eV}} = 2.92\times10^{18}\;\text{photons/s}\]This is why photons feel like a continuous wave in everyday life — only when intensity drops to a few photons per second (as in modern single-photon detectors) does the granular nature stand out.
11.12 Compton Scattering — Conclusive Evidence (1923)
Arthur Compton directed monochromatic X-rays at a graphite target and measured the wavelength of the scattered rays as a function of scattering angle. He observed that the scattered radiation contained two components:
- A peak at the original wavelength λ (electrons tightly bound to atoms — they recoil as a whole atom, virtually no wavelength shift).
- A peak at a slightly longer wavelength λ′ — light has lost energy. The shift Δλ depends only on the scattering angle θ:
This is exactly what one calculates by treating the X-ray as a photon of momentum \(h/\lambda\) elastically colliding with a free electron and applying conservation of energy and momentum. Wave optics offers no explanation for the wavelength shift. Compton received the Nobel Prize in 1927.
11.13 Photon "Mass" — Is There Such a Thing?
Photons travel at \(c\); special relativity says any particle with non-zero rest mass would need infinite energy to reach this speed. So a photon's rest mass is zero. It does, however, possess an effective relativistic mass obtained from \(E = mc^2\):
\[m = \frac{E}{c^2} = \frac{h\nu}{c^2} = \frac{h}{\lambda c}\]This effective mass is responsible for the photon's gravitational deflection (predicted by Einstein, confirmed at the 1919 solar eclipse). For a 500 nm photon: \(m \approx 4.4\times10^{-36}\) kg — about 200,000 times lighter than the electron.
Key idea — wave–particle duality: Light shows wave behaviour (interference, diffraction) and particle behaviour (photoelectric effect, Compton scattering). It is not "really" one or the other; depending on the experiment, one face shows. This duality, and de Broglie's symmetric proposal for matter, are the foundations of quantum theory.
Activity 11.3 — Counting Photons in Sunlight
Sunlight reaching the Earth's surface delivers roughly 1000 W per square metre. Suppose the average wavelength is taken to be 550 nm (green, near peak of solar spectrum). Estimate how many photons strike each square millimetre of skin every second.
Predict: Will it be a million? A billion? More?
Power per mm² = 1000 W/m² × 10⁻⁶ m²/mm² = 1.0 × 10⁻³ W.
Photon energy at 550 nm = 1240/550 = 2.25 eV = 3.61 × 10⁻¹⁹ J.
N = P/E = 10⁻³ / 3.61×10⁻¹⁹ = 2.77 × 10¹⁵ photons mm⁻² s⁻¹ — almost three quadrillion every second on a fingernail-sized patch! No wonder the granular nature of light hides so well.
Photon energy at 550 nm = 1240/550 = 2.25 eV = 3.61 × 10⁻¹⁹ J.
N = P/E = 10⁻³ / 3.61×10⁻¹⁹ = 2.77 × 10¹⁵ photons mm⁻² s⁻¹ — almost three quadrillion every second on a fingernail-sized patch! No wonder the granular nature of light hides so well.
Interactive — Photon Energy & Momentum Across the EM Spectrum
Slide through the wavelength scale from radio waves to γ-rays and watch how the photon's energy, frequency, momentum and effective mass all change together. Notice the colossal range — eighteen orders of magnitude.
ν
E (eV)
p (kg·m/s)
Effective m (kg)
Worked Examples
Example 1 — Photon energy of monochromatic 632.8 nm light
Find the energy and momentum of a photon emitted by a He-Ne laser of wavelength λ = 632.8 nm.
\(E = hc/\lambda = (6.626\times10^{-34})(3\times10^{8})/632.8\times10^{-9} = 3.14\times10^{-19}\) J = 1.96 eV.
\(p = h/\lambda = 6.626\times10^{-34}/632.8\times10^{-9} = 1.05\times10^{-27}\) kg·m/s.
\(p = h/\lambda = 6.626\times10^{-34}/632.8\times10^{-9} = 1.05\times10^{-27}\) kg·m/s.
Example 2 — Photon flux of a laser pointer
A 1-mW red laser (λ = 632.8 nm) shines on a wall. How many photons strike the wall per second?
N = P/(hν) = (10⁻³ W)/(3.14×10⁻¹⁹ J) ≈ 3.18×10¹⁵ photons/s.
Example 3 — Effective mass of a γ-ray photon
A nuclear γ-ray photon has energy 1.0 MeV. Find its frequency, wavelength, momentum and effective relativistic mass.
\(E = 1.0\) MeV = 1.6×10⁻¹³ J. \(\nu = E/h = 2.42\times10^{20}\) Hz.
\(\lambda = c/\nu = 1.24\times10^{-12}\) m = 1.24 pm.
\(p = E/c = 5.33\times10^{-22}\) kg·m/s.
\(m = E/c^{2} = 1.78\times10^{-30}\) kg — about twice the electron rest mass!
\(\lambda = c/\nu = 1.24\times10^{-12}\) m = 1.24 pm.
\(p = E/c = 5.33\times10^{-22}\) kg·m/s.
\(m = E/c^{2} = 1.78\times10^{-30}\) kg — about twice the electron rest mass!
Example 4 — Compton wavelength shift
A 0.1 nm X-ray photon scatters off an electron through 90°. Find the wavelength of the scattered photon.
Compton wavelength of the electron: \(h/m_ec = 2.43\times10^{-12}\) m.
\(\Delta\lambda = (2.43\times10^{-12})(1-\cos90°) = 2.43\times10^{-12}\) m.
\(\lambda' = 0.1\times10^{-9} + 2.43\times10^{-12} = 1.024\times10^{-10}\) m ≈ 0.1024 nm.
\(\Delta\lambda = (2.43\times10^{-12})(1-\cos90°) = 2.43\times10^{-12}\) m.
\(\lambda' = 0.1\times10^{-9} + 2.43\times10^{-12} = 1.024\times10^{-10}\) m ≈ 0.1024 nm.
Competency-Based Questions
Q1. The momentum of a photon of wavelength λ is:
(b) p = E/c = (hc/λ)/c = h/λ.
Q2. Which of the following is true for a photon?
(c) Photons always travel at c in vacuum; they are massless (rest), chargeless and never at rest.
Q3. (Short Answer) A red lamp and a blue lamp emit equal power. Which produces more photons per second, and why?
The red lamp. Each red photon (longer λ) carries less energy hν, so a given power P = N(hν) requires a larger N for red than for blue.
Q4. (True/False) The intensity of a beam of monochromatic light is proportional to the energy of each photon.
False. Intensity is N×hν per area per second. For a given frequency, intensity is set only by N (number of photons), since hν is fixed.
Q5. (HOT) An X-ray photon of wavelength 0.05 nm carries how many times more momentum than a visible photon of wavelength 500 nm?
p ∝ 1/λ. Ratio = 500/0.05 = 10⁴. The X-ray photon has 10,000 times the momentum of the visible photon.
Assertion–Reason Questions
Options: (A) Both true, R correct explanation of A. (B) Both true, R not the correct explanation. (C) A true, R false. (D) A false, R true.
Assertion: Photons are not deflected by electric and magnetic fields.
Reason: Photons are electrically neutral.
(A) Both true and the reason is the correct explanation. The Lorentz force qE + qv×B vanishes for q = 0.
Assertion: Compton scattering proves the particle nature of light.
Reason: The wavelength of scattered radiation is independent of scattering angle.
(C) Assertion is true, reason is false. The Compton shift Δλ depends explicitly on θ, and that is exactly what the photon model predicts.
Assertion: Even though a photon has zero rest mass, it has non-zero momentum.
Reason: Momentum and energy are linked by p = E/c for any massless particle moving at the speed of light.
(A) Both correct and the reason explains the assertion. Massless particles still carry momentum because they travel at c.
Frequently Asked Questions - Particle Nature Light
What is the main concept covered in Particle Nature Light?
In NCERT Class 12 Physics Chapter 11 (Dual Nature of Radiation and Matter), "Particle Nature Light" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Particle Nature Light useful in real-life applications?
Real-life applications of "Particle Nature Light" from NCERT Class 12 Physics Chapter 11 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Particle Nature Light?
Key formulas in "Particle Nature Light" (NCERT Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 11?
NCERT Class 12 Physics Chapter 11 (Dual Nature of Radiation and Matter) is structured so each part builds on the previous one. "Particle Nature Light" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Particle Nature Light?
CBSE board questions from "Particle Nature Light" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Particle Nature Light" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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