Digestive System

Introduction

Modern Physics covers the discoveries that overturned classical mechanics at the atomic and subatomic scale — from the internal structure of the atom to the behaviour of radioactive nuclei, the puzzling photoelectric effect, and the physics of nuclear reactors. It also includes the semiconductor revolution that underpins every electronic device, and the LASER that transformed communications and medicine.

NDA questions in this chapter are almost entirely conceptual. The examiner does not set complex quantum-mechanical calculations. Instead, the focus is on: which atomic model discovered what, the properties and comparisons of alpha, beta, and gamma rays, how nuclear fission differs from fusion, the photoelectric effect principle, semiconductor behaviour (including the p-n junction diode), and the X-ray properties. This is a concept-and-recall chapter where a structured understanding of a relatively small number of facts yields very high NDA scores.

NDA Exam Pattern Insight

Most frequently tested: Alpha, beta, gamma rays — properties, penetrating power, ionising power, deflection in fields; nuclear fission vs fusion; Rutherford’s alpha-scattering experiment and discovery of the nucleus; photoelectric effect and who explained it (Einstein); X-ray wavelength order and properties; semiconductor types (p-type: majority carriers = holes; n-type: majority carriers = electrons); LED and solar cell definitions; Bohr model ionisation energy.

Major conceptual traps: Gamma rays are electromagnetic (NOT particles). Alpha rays are deflected by electric AND magnetic fields; gamma rays are NOT deflected by either. The Sun’s energy comes from nuclear FUSION, not fission. X-rays travel at the same speed as gamma rays (both are EM waves). The nucleus contains protons AND neutrons (NOT electrons). In a p-n junction diode, current passes in one direction only — the NOT correct answer is always the option that implies bidirectional conduction.

Most common numerical themes: Half-life calculations (how much remains after n half-lives); X-ray wavelength identification; hydrogen ground state ionisation energy (13.6 eV); energy per photon comparisons (X-rays > UV > visible > IR > microwaves > radio waves).

Understand the Topic

Plant Cell vs Animal Cell

Understand the Topic

Topic Family	Key Concepts	Primary NDA Test Mode
Atomic Models	Thomson plum-pudding; Rutherford nucleus discovery; Bohr energy levels	Identification + comparison MCQ
Bohr Model	Energy levels, ground state, excited state, emission/absorption; ionisation energy 13.6 eV	Direct recall + conceptual
Atomic Spectra	Emission vs absorption spectrum; line spectra; shortest wavelength transition	Conceptual MCQ
Photoelectric Effect	Light ejects electrons; Einstein’s explanation; threshold frequency; work function	Conceptual MCQ (high)
X-Rays	EM wave, wavelength ~1 Å, produced by electron bombardment on metal target, heat at target	Properties MCQ (high)
Radioactivity	Alpha (He nucleus), beta (electron), gamma (EM wave); properties; GM counter	Comparison MCQ (very high)
Half-Life	Time for activity to halve; simple calculations after n half-lives	Numerical
Nuclear Fission	Heavy nucleus splits; chain reaction; reactor uses controlled fission	Conceptual MCQ
Nuclear Fusion	Light nuclei combine; Sun’s energy; H-bomb; needs higher temperature	Conceptual MCQ
Semiconductors	Conductor vs insulator vs semiconductor; intrinsic vs extrinsic; p-type (holes), n-type (electrons)	Classification MCQ
Diode / p-n Junction	Current in one direction only; polarity reversal stops current	Conceptual MCQ
LED / Solar Cell	LED: electrical → light energy; solar cell: light → electrical energy	Device identification MCQ
LASER	Stimulated emission; coherent light; monochromatic; highly directional	Properties MCQ

Highest Yield Areas: Alpha/beta/gamma comparison, nuclear fission vs fusion, photoelectric effect, X-ray properties, Rutherford’s experiment, p-n junction diode, LED vs solar cell, and the hydrogen atom ionisation energy — together these account for over 75% of NDA Modern Physics questions.

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Core Concepts

Atomic Models

Thomson’s Model (1897): Thomson proposed that an atom is a sphere of positive charge with electrons embedded in it — like raisins in a pudding. This is the “plum-pudding model.” It correctly identified electrons as constituents of atoms but incorrectly placed the positive charge uniformly throughout.

Rutherford’s Model (1911): Ernest Rutherford’s famous alpha-particle scattering experiment bombarded a thin gold foil with alpha particles. Most passed straight through, but a few were deflected at large angles and some bounced back. This proved: most of the atom is empty space; almost all the mass and all the positive charge are concentrated in a tiny, dense nucleus at the centre.

💡 Key Fact — NDA 2017-I Q. 60 and NDA 2021-II Q. 120 “Rutherford’s alpha-particle scattering experiment was responsible for the discovery of ___?” Answer: (c) Nucleus (not electron, not proton, not helium). The experiment revealed that the positive charge and most of the mass are concentrated in an extremely small central nucleus.

💡 Key Fact — NDA 2015-II Q. 115 “Which statement is correct?” (c) The atomic number of an element = number of protons in the nucleus of its atom. This is always true. Statement (d) “mass number = number of electrons” is wrong — mass number = protons + neutrons.

💡 Key Fact — NDA 2010-I Q. 115 “Which is correct about the nucleus?” Answer: (d) Both protons and neutrons can reside inside the nucleus. Electrons do NOT reside in the nucleus. The nucleus contains protons (positively charged) and neutrons (uncharged).

Bohr’s Model (1913): Niels Bohr proposed that electrons orbit the nucleus in specific allowed circular orbits (energy levels) without radiating energy. When an electron jumps from a higher energy level to a lower one, it emits a photon of light. When it absorbs energy, it jumps to a higher level.

• Ground state: Lowest energy level (n = 1) — most stable configuration
• Excited state: Any energy level above the ground state (n = 2, 3, 4…)
• Electrons can jump between levels by absorbing or emitting photons

💡 Key Fact — NDA 2017-II Q. 79 “Ionisation energy of hydrogen atom in the ground state is ___?” Answer: (b) 13.6 eV — not MeV, not Joule. The energy required to completely remove the electron from a hydrogen atom in its ground state is exactly 13.6 electron-volts (eV). This is one of the most tested values in NDA Modern Physics.

⚠️ NDA Trap — NDA 2019-II Q. 87 “Which statement about cathode rays is NOT correct?” Option (b): Cathode ray particles start from anode and move towards cathode. — This is WRONG. Cathode rays (electrons) start from the cathode (negative electrode) and move toward the anode (positive electrode). The name “cathode ray” itself indicates they originate from the cathode.

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Atomic Spectra

When atoms absorb or emit energy, they produce characteristic line spectra.

Emission Spectrum: When excited atoms return to lower energy states, they emit photons of specific wavelengths → bright lines on a dark background.

Absorption Spectrum: When white light passes through a cool gas, atoms absorb specific wavelengths → dark lines on a continuous bright background (identical wavelengths to emission, but missing from the spectrum).

Shortest wavelength emission — highest energy transition:

💡 Key Fact — NDA 2012-I Q. 93 “Which electron transition in hydrogen emits radiation of the shortest wavelength?” Answer: (a) n = 2 to n = 1. The n = 2 → n = 1 transition involves the largest energy difference (since n = 1 is the ground state). Larger energy difference → shorter wavelength (E = hf = hc/λ → higher E means shorter λ). Among the options given, n=2→1 produces the shortest wavelength (Lyman series).

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Photoelectric Effect

When light of sufficient frequency falls on a metal surface, electrons are ejected from the surface. This is the photoelectric effect.

Key principles (NDA level):

• Light must be above a threshold frequency (ν₀) to eject electrons — below this, no electrons are emitted regardless of intensity
• The work function (W₀) is the minimum energy needed to eject an electron from the metal surface
• Albert Einstein explained the photoelectric effect using the concept of photons (light quanta) — he received the Nobel Prize for this (not for relativity)
• Increasing the intensity of light increases the number of photoelectrons, but NOT their maximum kinetic energy
• Increasing the frequency increases the kinetic energy of ejected electrons

💡 Key Fact — NDA 2017-II Q. 73 “Electron emission from metallic surface by application of light is known as ___?” Answer: (b) Photoelectric emission. Not thermionic emission (that uses heat), not high field emission (uses strong electric field), not autoelectronic emission.

💡 Key Fact — NDA 2019-I Q. 85 “Who explained the phenomenon of photoelectric effect?” Answer: (b) Albert Einstein. Not Max Planck (who quantised energy but didn’t explain photoelectric effect), not Bohr (who explained atomic spectra), not Rutherford (who discovered the nucleus).

⚠️ NDA Trap — Photoelectric Effect and Intensity “Increasing the intensity of light increases the kinetic energy of emitted electrons.” — Wrong. Intensity (brightness) increases the NUMBER of emitted electrons (current), but not their maximum kinetic energy. Kinetic energy depends only on the frequency of the incident light. This is the most common photoelectric misconception.

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X-Rays

X-rays are electromagnetic radiation with very short wavelengths — shorter than ultraviolet light.

Key properties of X-rays:

• Electromagnetic waves (NOT particles)
• Travel at the speed of light (3 × 10⁸ m/s) — same as gamma rays and visible light
• Wavelength ≈ 1 Ångström (1 Å = 10⁻¹⁰ m)
• Produced by bombarding a metal target with high-energy electrons
• When produced, heat is generated at the target (most of the energy goes to heat)
• Can penetrate soft tissue but are stopped by dense materials (bone, lead)
• High-energy photons — more energetic than visible light and UV

Uses of X-rays: Medical imaging (bones), detecting cracks in metal structures, airport security scanners, cancer radiotherapy.

NOT used for: Radar systems (X-rays have too short a wavelength for radar; radio waves are used for radar).

💡 Key Fact — NDA 2010-I Q. 116 “Ratio of velocity of X-rays to gamma rays?” Answer: (c) is 1. Both X-rays and gamma rays are electromagnetic waves. All electromagnetic waves travel at the same speed (3 × 10⁸ m/s) in vacuum. The ratio is therefore 1:1.

💡 Key Fact — NDA 2010-I Q. 117 “Which pair of rays is electromagnetic in nature?” Answer: (d) X-rays and gamma rays. Both are electromagnetic waves. Alpha and beta rays are particle radiation. Cathode rays are electron beams (particles). Only X-rays and gamma rays are EM radiation in the given options.

💡 Key Fact — NDA 2010-I Q. 120 “When X-rays are produced ___?” Answer: (a) heat is generated at the target. When high-speed electrons bombard the metal target, most kinetic energy converts to heat; only a small fraction (about 1%) becomes X-ray radiation. The target gets very hot.

💡 Key Fact — NDA 2018-II Q. 108 “Wavelength of X-rays is of the order of ___?” Answer: (a) 1 Å (1 Ångström = 10⁻¹⁰ m). Not μm (micrometre = 10⁻⁶ m, that’s infrared/visible), not mm, not cm. X-rays sit between ultraviolet (10⁻⁸ m) and gamma rays (10⁻¹¹ m) in the electromagnetic spectrum.

💡 Key Fact — NDA 2022-II Q. 65 “Which wavelength corresponds to X-rays?” Answer: (d) 1 nm (10⁻⁹ m). Well, 1 nm is at the boundary of UV/soft X-ray range. Standard NDA answer: X-ray wavelength ~ 10⁻¹⁰ m = 1 Å = 0.1 nm. The option closest to the X-ray range is 1 nm (not 500 nm visible, not 5000 nm infrared, not 100 nm UV boundary). Answer: (d) 1 nm.

💡 Key Fact — NDA 2023-I Q. 91 “Which statement about X-rays is NOT true?” Answer: (c) Due to their shorter wavelengths, X-rays can be used for radar systems. — WRONG. Radar uses radio waves (long wavelengths, 1 mm to 1 m). X-rays are not suitable for radar. The other statements are correct: X-ray wavelengths ≈ 1 Å ✓, produced by electron bombardment of metal target ✓, used for cancer treatment ✓.

💡 Key Fact — NDA 2017-II Q. 114 “Which wave carries maximum energy per photon?” Answer: (a) X-rays. Energy of a photon E = hf. Higher frequency = higher energy. In order: Radio < Microwave < Infrared < Visible light < UV < X-rays < Gamma rays. X-rays have the highest energy per photon among the options given.

💡 Key Fact — NDA 2018-II Q. 90 X-rays, UV, and visible light photon energy comparison: Statement 1: Wavelength of visible light > wavelength of X-rays ✓ (visible ≈ 400–700 nm; X-ray ≈ 0.01–10 nm) Statement 2: Energy of X-ray photons > energy of UV photons ✓ (shorter wavelength = more energy) Statement 3: Energy of UV photons < energy of visible light photons ✗ (UV has shorter wavelength than visible = MORE energy than visible) Correct statements: 1 and 2 only. Answer: (b) 1 and 2 only.

💡 Key Fact — NDA 2017-I Q. 122 “X-ray tube: potential difference doubled. Cutoff wavelength?” Answer: (c) Will be halved. Higher potential difference → electrons have more energy → X-rays have more energy → shorter wavelength (E ∝ 1/λ). Doubling potential difference doubles energy → halves minimum wavelength.

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Radioactivity

Radioactivity is the spontaneous disintegration of unstable atomic nuclei, accompanied by emission of radiation. It was discovered by Henri Becquerel (1896) and further studied by Marie Curie.

The three types of radiation:

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Particle (Helium nucleus: 2 protons + 2 neutrons)	Particle (High-speed electron)	Electromagnetic wave (photon)
Charge	+2	−1	0 (neutral)
Mass	4 atomic mass units	~1/1836 of proton mass	Zero (massless)
Ionising power	Highest	Medium	Lowest
Penetrating power	Lowest (stopped by paper or skin)	Medium (stopped by 3–5 mm aluminium)	Highest (needs several cm of lead or concrete)
Speed	Slowest (~10⁷ m/s)	Faster (~up to 0.99c)	Speed of light (c)
Deflection in electric field	Yes (toward negative plate)	Yes (toward positive plate)	No deflection
Deflection in magnetic field	Yes	Yes	No deflection
Effect on nucleus	Loses 2 protons, 2 neutrons (Z−2, A−4)	Gains 1 proton (Z+1, A unchanged)	No change in Z or A

⚠️ NDA Trap — Gamma Rays are NOT Deflected Gamma rays are electromagnetic waves with no charge. They are NOT deflected by electric or magnetic fields. Alpha and beta particles carry charge and ARE deflected. The NDA repeatedly tests this as the “NOT deflected by fields” option. Gamma ray = electromagnetic = no deflection.

⚠️ NDA Trap — Penetrating Power vs Ionising Power Are Opposite Alpha has the HIGHEST ionising power but LOWEST penetrating power. Gamma has the LOWEST ionising power but HIGHEST penetrating power. This is because: alphas are heavy, slow, and interact strongly with matter (ionise a lot but don’t travel far). Gammas are massless, travel at light speed, and interact weakly (penetrate far but ionise less).

Measurement of radioactivity: The Geiger-Müller (GM) Counter is used to detect and measure radioactivity.

💡 Key Fact — NDA 2017-II Q. 75 “Radioactivity is measured by ___?” Answer: (a) GM Counter (Geiger-Müller Counter). Not polarimeter, not calorimeter, not colorimeter.

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Half-Life

Half-life (T₁/₂) is the time required for exactly half of the radioactive nuclei in a sample to decay.

After each half-life, the amount of remaining radioactive material halves:

Number of Half-Lives	Fraction Remaining
0	1 (100%)
1	1/2 (50%)
2	1/4 (25%)
3	1/8 (12.5%)
n	(1/2)ⁿ

Formula: N = N₀ × (1/2)^(t/T₁/₂)

where N is the remaining amount, N₀ is the initial amount, t is elapsed time, T₁/₂ is the half-life.

⚠️ NDA Trap — Half-Life Misconception “After two half-lives, the substance completely decays.” — Wrong. After two half-lives, 1/4 (25%) remains. After four half-lives, 1/16 (about 6%) remains. Radioactive decay follows exponential decay — the substance never completely reaches zero in a finite time.

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Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus (like uranium-235 or plutonium-239) into two or more smaller nuclei, accompanied by the release of a large amount of energy and 2–3 neutrons.

Chain Reaction: The neutrons released by one fission event trigger additional fission events. In a controlled chain reaction (nuclear reactor), the rate is maintained steady. In an uncontrolled chain reaction (atomic bomb), the rate grows exponentially.

💡 Key Fact — NDA 2019-I Q. 81 “Basic scientific principle behind a nuclear reactor?” Answer: (d) Controlled nuclear fission. Not fusion (too difficult to sustain), not uncontrolled fission (that’s an atomic bomb). A nuclear reactor uses controlled fission to generate heat, which produces steam to drive turbines.

💡 Key Fact — NDA 2019-I Q. 60 “Which mineral is used as fuel in nuclear power stations?” Answer: (d) Pitchblende. Pitchblende is the ore that contains uranium — the primary fuel for nuclear reactors. Bauxite = aluminium ore; Quartz = silicon dioxide; Feldspar = silicate mineral.

Fission releases much more energy per atom than any chemical reaction. The energy source is the mass defect — a tiny amount of mass converts to energy according to E = mc².

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Nuclear Fusion

Nuclear fusion is the combining of two light nuclei (such as isotopes of hydrogen — deuterium and tritium) into a heavier nucleus, releasing enormous energy.

Fusion requires extremely high temperatures (millions of degrees Celsius) and extreme pressure to force nuclei close enough for the nuclear force to overcome the electrostatic repulsion between them.

The Sun’s energy comes from nuclear fusion:

💡 Key Fact — NDA 2010-II Q. 147 “The Sun’s temperature remains constant despite constant radiation. This is because of ___?” Answer: (c) fusion. The Sun continuously fuses hydrogen into helium in its core, releasing energy that replaces what is lost as radiation.

💡 Key Fact — NDA 2013-I Q. 64 “Sequence for solar energy generation?” Correct sequence: 1 → 3 → 2: Hydrogen converts to helium at high temperature and pressure (1); this generates a vast quantity of energy by nuclear fusion (3); the energy finds its way to the Sun’s surface (2). Answer: (d) 1-3-2.

Applications of fusion:

• Hydrogen Bomb (H-bomb): Uncontrolled fusion triggered by a fission bomb (to achieve the required temperature)
• Future clean energy: Controlled fusion reactors (still under development — projects like ITER)

Fusion vs Fission — Energy comparison: Fusion releases more energy per unit mass of fuel than fission. However, fusion requires higher temperatures to initiate and is harder to control.

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Semiconductors

A semiconductor is a material whose electrical conductivity falls between conductors (metals) and insulators, and which can be altered by temperature, impurities, or light.

Band theory classification:

Property	Conductors (Metals)	Semiconductors	Insulators
Examples	Copper, silver, gold	Silicon, germanium, carbon (graphite)	Rubber, glass, wood, plastic
Band gap	None (overlapping bands)	Small (0.1–3 eV)	Large (> 5 eV)
Conductivity	Very high	Moderate	Very low
Effect of temperature	Decreases (resistance increases)	Increases (resistance decreases)	Very slight increase
Primary charge carriers	Free electrons	Electrons and holes	None (very few)
NDA relevance	Resistance, Ohm’s Law	Diode, LED, solar cell	Fuse, insulation

⚠️ NDA Trap — Temperature Effect on Semiconductors For metals: resistance INCREASES with temperature. For semiconductors: resistance DECREASES with temperature (conductivity increases). This is opposite behaviour and is a classic NDA trap.

Intrinsic Semiconductor: Pure semiconductor (silicon or germanium) with equal numbers of electrons and holes as charge carriers.

Extrinsic Semiconductor: Impurity-doped semiconductor.

• n-type: Doped with pentavalent impurity (phosphorus, arsenic). Majority carriers = free electrons (negative). Minority = holes.
• p-type: Doped with trivalent impurity (boron, aluminium). Majority carriers = holes (positive). Minority = electrons.

💡 Key Fact — NDA 2017-II Q. 78 “Majority charge carriers in p-type semiconductor are ___?” Answer: (d) holes. Not free electrons (that’s n-type), not conduction electrons, not ions. In p-type semiconductors, the dopant creates positive holes as majority carriers.

p-n Junction Diode: A p-n junction is formed when p-type and n-type semiconductors are joined. In forward bias (positive terminal to p-side), current flows freely. In reverse bias (positive terminal to n-side), current is blocked. The diode allows current in ONE direction only.

💡 Key Fact — NDA 2014-I Q. 141 “Semiconductor device in series with battery and resistance. Current flows normally, but when battery polarity is reversed, current drops to zero. The device is ___?” Answer: (d) p-n junction. A p-n junction diode conducts in one direction (forward bias) and blocks in the other (reverse bias). None of the other options (p-type alone, n-type alone, intrinsic alone) would show this one-directional property.

LED (Light Emitting Diode): An LED is a forward-biased p-n junction diode that emits light when current flows through it. Energy is released as photons when electrons recombine with holes.

Energy conversion: Electrical energy → Light energy

💡 Key Fact — NDA 2018-II Q. 71 “Full form of LED is ___?” Answer: (a) Light Emitting Diode. Tested twice in NDA 2018-II and NDA 2021-I. Not “Light Emitting Device,” not “Light Enhancing Diode.”

💡 Key Fact — NDA 2021-I Q. 54 “LED stands for ___?” Answer: (c) Light Emitting Diode. Same fact, different paper.

💡 Key Fact — NDA 2012-II Q. 99 Power consumption for equal light intensity, from lowest to highest: Answer: (b) LED < CFL < Fluorescent tube < Incandescent bulb. LEDs are the most energy-efficient light source.

Solar Cell (Photovoltaic Cell): A solar cell converts light energy (photons) into electrical energy using the photovoltaic effect — a specific case of the photoelectric effect in semiconductors.

Energy conversion: Light energy → Electrical energy

💡 Key Fact — NDA 2022-II Q. 136 “In which device is light energy converted into electrical energy?” Answer: (c) Solar cell. Not LED (converts electrical to light), not LED diode, not transistor. Solar cell = photovoltaic cell = light → electricity.

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LASER

LASER stands for Light Amplification by Stimulated Emission of Radiation.

Principle: Photons stimulate excited atoms to emit additional identical photons — producing an amplified beam.

Properties of laser light:

• Monochromatic: Single wavelength (one pure colour)
• Coherent: All photons in phase (crests and troughs align)
• Highly directional: Very narrow, non-diverging beam
• High intensity: Energy concentrated in a narrow beam

Applications: Surgery, communications (optical fibre), barcode readers, CD/DVD players, laser printers, military rangefinding, welding.

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Tables & Comparisons

Thomson vs Rutherford vs Bohr Model

Feature	Thomson Model	Rutherford Model	Bohr Model
Proposed by	J.J. Thomson (1897)	Ernest Rutherford (1911)	Niels Bohr (1913)
Also called	Plum-pudding model	Nuclear model	Planetary model (quantised)
Positive charge location	Spread throughout atom	Concentrated in nucleus	Concentrated in nucleus
Electron location	Embedded throughout	Orbiting nucleus	Fixed orbits (energy levels)
Nucleus concept	No — no nucleus	Yes — discovered nucleus	Yes — nucleus
Explained	Existence of electrons	Atomic nucleus	Atomic spectra; energy levels
Discovery from	Cathode ray experiments	Alpha-particle scattering	Spectral lines of hydrogen

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Alpha vs Beta vs Gamma Rays — The Master Table

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus (²⁴He)	High-speed electron (e⁻)	Electromagnetic radiation
Charge	+2	−1	Zero
Mass (a.m.u.)	4	~1/1836	Zero
Ionising power	Highest	Medium	Lowest
Penetrating power	Lowest — stopped by paper	Medium — stopped by Al (few mm)	Highest — needs lead or concrete
Speed	~5–7% of c	Up to ~99% of c	c (speed of light)
Deflection in E/B field	Yes — deflected	Yes — deflected (opposite direction)	No — not deflected
Effect on nucleus	Z decreases by 2, A decreases by 4	Z increases by 1, A unchanged	Z and A unchanged

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Nuclear Fission vs Fusion

Property	Nuclear Fission	Nuclear Fusion
Process	Heavy nucleus splits into lighter nuclei	Light nuclei combine to form heavier nucleus
Fuel	Uranium-235, Plutonium-239	Hydrogen isotopes (deuterium, tritium)
Temperature required	Moderate (achievable in reactors)	Extremely high (millions °C — plasma)
Energy released	Very large	Even larger per unit mass
Neutrons produced	2–3 neutrons per event	None (or fewer byproducts)
Radiation produced	Alpha, beta, gamma + neutron	Fewer radioactive byproducts
Applications	Nuclear reactor, atomic bomb	Sun, H-bomb, future ITER reactor
Chain reaction	Yes (self-sustaining with U-235)	No self-sustaining chain reaction
Controlled use	Yes — nuclear power plants	Not yet (research stage)

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Conductors vs Semiconductors vs Insulators

Property	Conductors	Semiconductors	Insulators
Examples	Cu, Ag, Al, Fe	Si, Ge, C (graphite)	Glass, rubber, wood, plastic
Free electrons	Very many	Few	Essentially none
Conductivity	Very high	Moderate	Very low
Resistivity	Very low (10⁻⁸ Ω·m)	Moderate (10⁻⁴ to 10⁴ Ω·m)	Very high (10⁸ to 10¹⁵ Ω·m)
Temperature effect	Resistance increases	Resistance decreases	Barely changes
Energy band gap	None (zero)	Small (0.1–3 eV)	Large (>5 eV)
Uses	Wiring, switches	Diodes, transistors, solar cells	Insulation, capacitor dielectric

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Emission vs Absorption Spectrum

Property	Emission Spectrum	Absorption Spectrum
How produced	Excited atoms release photons	Cool gas absorbs specific wavelengths from white light
Appearance	Bright coloured lines on dark background	Dark lines on rainbow (continuous) background
What it shows	Energies emitted when electrons fall to lower levels	Energies absorbed when electrons jump to higher levels
Wavelengths	Same set of wavelengths as absorption spectrum	Same set as emission spectrum (but absent from white light)
Example	Neon sign glow	Solar absorption spectrum (Fraunhofer lines)

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LASER vs Ordinary Light

Property	LASER	Ordinary Light
Wavelength	Single (monochromatic)	Multiple (polychromatic)
Phase	Coherent (all in phase)	Incoherent (random phases)
Directionality	Highly directional (narrow beam)	Spreads in all directions
Intensity	Very high (concentrated beam)	Lower
Origin	Stimulated emission	Spontaneous emission
Uses	Surgery, fibre optics, barcode scanning	General illumination

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Formulas

Formula 1 — Half-Life Decay

N = N₀ × (1/2)^n where n = t/T₁/₂

N	Number of radioactive nuclei remaining (or remaining mass/activity)
N₀	Initial number of nuclei (or initial mass/activity)
n	Number of half-lives elapsed = t/T₁/₂
T₁/₂	Half-life (in any time unit — must match t)

Used when: Finding how much radioactive material remains after a given time.

⚠️ NDA Trap: After every half-life, HALF remains. After n half-lives, (1/2)ⁿ remains. After 3 half-lives: (1/2)³ = 1/8 of original remains (not 1/6 or 1/3). The fraction always involves a power of 2.

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Formula 2 — Photoelectric Effect (Conceptual)

KE_max = hν − W₀ = hν − hν₀

KE_max	Maximum kinetic energy of emitted electrons (J or eV)
h	Planck’s constant = 6.626 × 10⁻³⁴ J·s
ν	Frequency of incident light (Hz)
W₀ = hν₀	Work function of the metal (minimum energy to eject electron)
ν₀	Threshold frequency (minimum frequency for photoelectric emission)

Used when: Calculating kinetic energy of emitted photoelectrons or threshold frequency.

⚠️ NDA Trap: For NDA, the conceptual form matters more than numerical calculation. Key: no emission if ν < ν₀. KE increases with frequency. KE does NOT increase with intensity (more electrons, same KE).

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Formula 3 — Energy of a Photon (Conceptual)

E = hν = hc/λ

E	Energy of a photon (J or eV)
h	Planck’s constant
ν	Frequency of radiation
c	Speed of light = 3 × 10⁸ m/s
λ	Wavelength

Key proportionality for NDA: Higher frequency → shorter wavelength → MORE energy per photon.

Energy order: Radio < Microwave < Infrared < Visible < UV < X-rays < Gamma rays

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Formula 4 — Remaining Activity After n Half-Lives

Remaining fraction = (1/2)ⁿ

Half-lives (n)	Fraction remaining	Percentage
1	1/2	50%
2	1/4	25%
3	1/8	12.5%
4	1/16	6.25%
10	1/1024	≈ 0.1%

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Worked NDA Numericals

NDA Context	Given	Formula	Answer
Half-Life: 8 g radioactive substance, T₁/₂ = 3 days. Amount after 9 days?	n = 9/3 = 3 half-lives; N₀ = 8 g	N = 8 × (1/2)³ = 8 × 1/8	1 g
Half-Life: 100 g, T₁/₂ = 1 hour. Amount after 4 hours?	n = 4/1 = 4 half-lives	N = 100 × (1/2)⁴ = 100/16	6.25 g
Hydrogen ionisation energy (direct recall)	Ground state hydrogen	Value = 13.6 eV	13.6 eV
X-ray cutoff wavelength: Potential doubled (NDA 2017-I). New wavelength?	λ ∝ 1/V; V doubled	λ_new = λ/2	Halved
Remaining after 3 half-lives	N₀, T₁/₂	Fraction = (1/2)³ = 1/8	1/8 of original
Photon energy ordering (NDA 2017-II)	X-rays vs Radio vs Light vs Microwaves	E = hν; X-rays have highest frequency	X-rays have maximum energy