JEE Advanced 2026 Paper 2 — Full Mock Test (54 Questions, 180 Marks)
Mathematics · Physics · Chemistry
This MCQ module is based on: Em Spectrum
TOPIC 36 OF 38
Em Spectrum
🎓 Class 12
Physics
CBSE
Theory
Ch 8 – Electromagnetic Waves
⏱ ~14 min
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Em Spectrum
8.7 The Electromagnetic Spectrum
Although all EM waves share the same fundamental nature (E ⊥ B, transverse, speed c in vacuum), they span an enormous range of wavelengths — from kilometres-long radio waves to gamma rays smaller than an atomic nucleus. The full range is called the electromagnetic spectrum.
| Band | Wavelength range | Frequency range | Source | Major use / detection |
|---|---|---|---|---|
| Radio waves | > 0.1 m | < 3 GHz | oscillating circuits / antennas | radio, TV, FM, AM, cellular |
| Microwaves | 1 mm - 0.1 m | 3-300 GHz | klystron, magnetron, Gunn diode | radar, microwave oven, satellite TV |
| Infrared (IR) | 700 nm - 1 mm | 3×10¹¹-4×10¹⁴ Hz | vibrations of molecules, hot bodies | night vision, remote controls, weather satellites, heating |
| Visible | 400-700 nm | 4×10¹⁴-7.5×10¹⁴ Hz | excited atoms, hot filaments, LED | vision, photography, optical fibre |
| Ultraviolet (UV) | 10-400 nm | 7.5×10¹⁴-3×10¹⁶ Hz | arc lamps, the Sun, mercury vapour | sterilisation, vitamin D, ozone formation |
| X-rays | 0.01-10 nm | 3×10¹⁶-3×10¹⁹ Hz | X-ray tubes (electron deceleration), inner-shell electron transitions | medical imaging, CT, crystallography, security |
| Gamma rays | < 0.01 nm | > 3×10¹⁹ Hz | nuclear transitions, radioactive decay, cosmic sources | cancer therapy, sterilisation, astrophysics |
8.7.1 Radio Waves
Produced by oscillating LC circuits driving an antenna. Sub-bands: LF/MF (300 kHz-3 MHz, AM radio), HF (3-30 MHz, shortwave), VHF (30-300 MHz, FM, TV), UHF (300 MHz-3 GHz, mobile phones, Wi-Fi 2.4 GHz). They reflect from the ionosphere allowing long-distance communication around the curve of the Earth.
8.7.2 Microwaves
Short-wavelength radio waves produced by special vacuum tubes (klystron, magnetron) and solid-state Gunn diodes. Used in radar (because their short λ gives sharp directional beams), satellite communication, mobile-phone backhaul and the kitchen microwave oven (2.45 GHz - tuned to a water-molecule rotational mode for efficient food heating).
8.7.3 Infrared (IR)
Emitted by every warm body. Range overlaps with molecular vibration energies, so IR is strongly absorbed by water vapour and CO₂ in the atmosphere — the basis of the greenhouse effect. Uses: night-vision goggles, TV remotes (~940 nm), thermal cameras for medical diagnosis and fire-fighting, optical-fibre data transmission at 1.55 μm.
8.7.4 Visible Light
The narrow band our eyes can detect, 400 nm (violet) to 700 nm (red). Produced by transitions of outer-shell electrons in atoms and by hot bodies. The colours of the rainbow lie within this single octave. The Sun emits its peak power here — and life on Earth evolved to exploit this peak.
8.7.5 Ultraviolet (UV)
Lies above visible at higher frequency. Sub-bands: UV-A (315-400 nm), UV-B (280-315 nm), UV-C (100-280 nm). The Sun is a strong UV source but the ozone layer absorbs almost all UV-B and UV-C, protecting life. Used in sterilising water, producing vitamin D in skin, fluorescence in CFL lamps and security marking on currency.
8.7.6 X-rays
Discovered by Roentgen in 1895. Produced when fast electrons decelerate sharply on hitting a metal target (bremsstrahlung) or when inner-shell electrons fall into vacancies. Their wavelengths are comparable to atomic spacings (≈ 0.1 nm) so they diffract from crystals (Bragg). Used in medical radiography, CT scans, crystallography, airport security and astronomy.
8.7.7 Gamma Rays
The most energetic EM radiation. Originate from nuclear transitions, radioactive decay, electron-positron annihilation and astrophysical sources (gamma-ray bursts, pulsars). Used in cancer therapy (precisely targeted gamma knife), food sterilisation, and as a probe of astrophysical processes.
Hierarchy of energy (E = hf): radio < microwaves < IR < visible < UV < X-rays < γ-rays. As energy per photon increases, the radiation becomes more penetrating and more capable of damaging biological tissue. UV, X and γ are "ionising" radiations.
Example 8.5 — Wavelength and band identification
An EM wave has frequency 6.0 × 10¹⁴ Hz. (a) Find its wavelength in vacuum. (b) Which band does it belong to?
(a) λ = c/f = 3 × 10⁸ / (6.0 × 10¹⁴) = 5.0 × 10⁻⁷ m = 500 nm.
(b) This is in the green region of the visible band (between 495 and 570 nm).
Example 8.6 — Photon energy of an X-ray
An X-ray photon has wavelength 0.1 nm. Find (a) its frequency, (b) photon energy in eV.
(a) f = c/λ = 3 × 10⁸ / 10⁻¹⁰ = 3 × 10¹⁸ Hz.
(b) E = hf = 6.63 × 10⁻³⁴ × 3 × 10¹⁸ = 1.99 × 10⁻¹⁵ J = (1.99 × 10⁻¹⁵)/(1.6 × 10⁻¹⁹) = 1.24 × 10⁴ eV ≈ 12.4 keV.
Example 8.7 — Why microwave ovens use 2.45 GHz
Calculate the wavelength of 2.45 GHz microwaves. Explain why the oven cavity is at least a few times this wavelength.
λ = 3×10⁸/2.45×10⁹ = 12.24 cm. A typical oven cavity is 30 cm wide ≈ 2.5 λ - large enough to set up standing waves and rotate the food (with a turntable) so that all parts pass through both nodes and antinodes for uniform heating.
Simulation: EM Spectrum Band Identifier
Move the slider to scan across the spectrum. The display shows the wavelength, frequency, photon energy and the band it belongs to.
| Wavelength λ | 500 nm |
| Frequency f | 6.0 × 10¹⁴ Hz |
| Photon energy E = hf | 2.48 eV |
| Band | Visible (green) |
| Typical source | excited atoms, LEDs, Sun |
Activity 8.3 — TV remote on a phone camera
Point any TV remote at the front camera of a smartphone, press a button while looking at the camera preview screen.
Predict: will you see anything in the preview, given that the remote's light is invisible to your eyes?
The remote's tip flashes purple-white on the camera preview! Phone camera sensors are sensitive to near-infrared (around 940 nm) which is beyond the human eye's range. Some newer phones have an IR-blocking filter that suppresses this effect on the rear camera, so always try the front camera.
Competency-Based Questions L1L2L3L4L6
An astronomer detects radiation of wavelength 21 cm from a hydrogen cloud in deep space, and from another source records wavelengths of 600 nm and 0.5 nm.
1. The 21 cm radiation belongs to which band? L1
(a) Radio (UHF). 21 cm corresponds to f = 1420 MHz - the famous "21 cm line" used in radio astronomy.
2. Order the three signals by photon energy (lowest to highest). L2
21 cm (radio) < 600 nm (visible) < 0.5 nm (X-ray). Shorter wavelength ⇒ higher frequency ⇒ higher photon energy E = hf.
3. Calculate the photon energy of the 600 nm visible signal (in eV). L3
E = hc/λ = (6.63×10⁻³⁴ × 3×10⁸)/(600×10⁻⁹) = 3.31×10⁻¹⁹ J = 3.31×10⁻¹⁹/1.6×10⁻¹⁹ = 2.07 eV.
4. Justify why X-rays are used for bone imaging but visible light is not. L4
X-ray photons have energy ≈ keV - high enough to penetrate soft tissue but be absorbed by denser bone (calcium). Visible light photons (≈ eV) lack penetration and are scattered or absorbed at the skin surface, giving no internal information. The contrast between soft tissue and bone is much higher for X-rays.
5. Propose two ways the EM spectrum can be used to remotely measure properties of the Sun. L6
(i) Analyse the visible/IR/UV spectrum and use Wien's law to estimate surface temperature (~5800 K). (ii) Detect radio emissions from the Sun's corona and X-ray flares to study magnetic activity. Other valid answers: gamma-ray spectroscopy of solar flares; spectroscopy of absorption lines (Fraunhofer) to identify elements.
Assertion-Reason Questions
Assertion: Radio waves and X-rays travel at the same speed in vacuum.
Reason: Both are electromagnetic waves and obey c = 1/√(μ₀ε₀) regardless of frequency.
(A). Both true; R explains A.
Assertion: Ozone in the upper atmosphere protects life from UV-B radiation.
Reason: UV-B photons have just the right energy to dissociate ozone molecules into O + O₂, getting absorbed in the process.
(A). Both true; R explains A.
Assertion: A microwave oven heats food but a radio receiver of the same power does not.
Reason: Microwave photons have lower energy than radio photons.
(C). A is true (microwaves resonate with water-molecule rotations, transferring energy efficiently). R is FALSE - microwave photons actually have HIGHER energy than radio photons.
Frequently Asked Questions - Em Spectrum
What is the main concept covered in Em Spectrum?
In NCERT Class 12 Physics Chapter 8 (Electromagnetic Waves), "Em Spectrum" 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 Em Spectrum useful in real-life applications?
Real-life applications of "Em Spectrum" from NCERT Class 12 Physics Chapter 8 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 Em Spectrum?
Key formulas in "Em Spectrum" (NCERT Class 12 Physics Chapter 8 Electromagnetic Waves) 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 8?
NCERT Class 12 Physics Chapter 8 (Electromagnetic Waves) is structured so each part builds on the previous one. "Em Spectrum" 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 Em Spectrum?
CBSE board questions from "Em Spectrum" 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 "Em Spectrum" 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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