Modern physics basics for NDA

Modern physics is thin in the NDA syllabus on paper, which names only the uses of X-rays among the electricity topics. In practice, GK questions reach further: alpha, beta and gamma rays, fission and fusion, nuclear reactors, the photoelectric effect, the electromagnetic spectrum and semiconductor devices. These overlap with the chemistry syllabus (atomic structure) and with current affairs on nuclear power and space.

The questions are nearly all factual and conceptual. Half-life, alpha and beta decay arithmetic, and E = mc² are the only numericals, and each takes a line. The challenge is precision: which radiation is most penetrating and which most ionising, what a moderator does versus a control rod, what intensity changes in the photoelectric effect and what it does not.

Typical question types are:

• discoverers of the electron, proton, neutron, nucleus, X-rays and radioactivity;
• isotopes, isobars and isotones;
• properties of alpha, beta and gamma radiation; changes in Z and A on decay;
• half-life problems;
• fission, chain reaction, reactor parts, fusion in the Sun;
• the photoelectric effect and photon energy;
• X-rays: production, properties and uses;
• the order and uses of the electromagnetic spectrum;
• lasers, semiconductors, doping, diodes and transistors.

The atom and the nucleus

Rutherford's experiment showed that almost all the mass and all the positive charge of an atom sit in a tiny nucleus, about 10⁻¹⁵ m across, while the atom is about 10⁻¹⁰ m across. The atom is mostly empty space.

The nucleus contains protons (positive) and neutrons (neutral), together called nucleons. Atomic number Z = number of protons; mass number A = protons + neutrons.

• Isotopes: same Z, different A. Hydrogen (¹H), deuterium (²H) and tritium (³H); carbon-12 and carbon-14; uranium-235 and uranium-238. Isotopes have the same chemical properties.
• Isobars: same A, different Z, such as argon-40 and calcium-40.
• Isotones: same number of neutrons, such as carbon-14 and oxygen-16 (8 neutrons each).

Radioactivity

Some heavy nuclei are unstable and emit radiation on their own, unaffected by temperature, pressure or chemical combination. Becquerel found this in uranium; Marie and Pierre Curie discovered polonium and radium.

Half-life is the time in which half the nuclei of a radioactive sample decay. It is fixed for each isotope. After n half-lives, the fraction left is (½)ⁿ: a half after one, a quarter after two, an eighth after three.

Uses of radioisotopes:

• Carbon-14 dating of old organic remains (half-life about 5,730 years).
• Cobalt-60 gamma rays in cancer therapy and to sterilise medical equipment and preserve food.
• Iodine-131 to diagnose and treat thyroid disorders.
• Tracers to study reactions, find leaks in pipelines and follow the uptake of fertilisers by plants.

Nuclear energy: fission and fusion

Einstein's E = mc² says mass and energy are interchangeable. A tiny loss of mass releases enormous energy because c² is so large: 1 g of mass is equivalent to 0.001 × (3 × 10⁸)² = 9 × 10¹³ J.

Fission: a heavy nucleus such as uranium-235 absorbs a slow neutron and splits into two medium nuclei (for example barium and krypton), releasing about 200 MeV and two or three fresh neutrons. Those neutrons can split more nuclei, giving a chain reaction. Uncontrolled, it is an atomic bomb; controlled, it runs a power reactor.

India's pressurised heavy water reactors (PHWRs) use natural uranium as fuel and heavy water as both moderator and coolant.

Fusion: light nuclei, such as isotopes of hydrogen, combine to form a heavier nucleus (helium), releasing even more energy per unit mass than fission. It needs temperatures of millions of degrees. Fusion powers the Sun and the stars and the hydrogen bomb. Fusion reactors for electricity are still experimental.

The photoelectric effect

When light of high enough frequency falls on a metal, electrons are emitted. Einstein explained this in 1905 by treating light as a stream of photons, each with energy E = hf (h is Planck's constant). He won the 1921 Nobel Prize in Physics for it.

• Below a threshold frequency, no electrons come out, however bright the light.
• The maximum kinetic energy of the electrons depends on the frequency, not the intensity.
• The number of electrons emitted depends on the intensity.
• Emission is practically instantaneous.

Since violet light has a higher frequency than red, a violet photon carries more energy than a red one. Photocells based on this effect are used in automatic doors, burglar alarms and light meters.

X-rays

X-rays are produced when fast electrons strike a heavy metal target such as tungsten, in an X-ray tube. They are electromagnetic waves of very short wavelength, so they travel at the speed of light, are not deflected by electric or magnetic fields, and penetrate matter that stops light.

Uses:

• Medical imaging: bones absorb X-rays more than flesh, so fractures show clearly; CT scans build cross-sections.
• Security: baggage screening at airports.
• Industry: detecting flaws and cracks in metal castings and welds.
• Science: X-ray diffraction reveals the arrangement of atoms in crystals.
• Radiotherapy for some cancers.

X-rays ionise living tissue, so exposure is kept to a minimum and radiographers use lead shielding.

The electromagnetic spectrum

All electromagnetic waves travel at 3 × 10⁸ m/s in a vacuum. In order of increasing frequency (decreasing wavelength):

Lasers and semiconductors

LASER stands for Light Amplification by Stimulated Emission of Radiation. Laser light is monochromatic (one wavelength), coherent and highly directional. It is used in eye surgery, barcode scanners, optical fibre communication, cutting and welding, and in military rangefinders and target designators.

Semiconductors such as silicon and germanium have conductivity between that of conductors and insulators, and their resistance falls as temperature rises. Adding tiny amounts of impurity (doping) changes this:

• n-type: doped with a pentavalent element such as phosphorus or arsenic; extra electrons carry the current.
• p-type: doped with a trivalent element such as boron, aluminium or gallium; "holes" carry the current.

A p–n junction diode conducts in one direction only (forward bias), so it is used as a rectifier to convert AC to DC. An LED is a diode that emits light; a solar cell is a junction that turns light into electricity; a Zener diode regulates voltage. A transistor amplifies signals and acts as a switch, and integrated circuits pack millions of transistors onto one chip.

Worked NDA-style MCQs

Q1. A radioactive sample of 32 g has a half-life of 5 days. After 20 days, the mass left is:
(a) 8 g (b) 4 g (c) 2 g (d) 1 g

20 days = 4 half-lives, so 32 × (½)⁴ = 32/16 = 2 g. Answer: (c).

Q2. Uranium-238 (Z = 92) emits one alpha particle. The new nucleus has:
(a) Z = 90, A = 234 (b) Z = 92, A = 234 (c) Z = 93, A = 238 (d) Z = 91, A = 236

Alpha emission lowers Z by 2 and A by 4. The product is thorium-234. Answer: (a).

Q3. When a nucleus emits a beta particle, its:
(a) mass number falls by 1 (b) atomic number rises by 1 (c) atomic number falls by 2 (d) nothing changes

A neutron turns into a proton and an electron; the electron leaves. A is unchanged. Answer: (b).

Q4. In the photoelectric effect, increasing the intensity of light (above the threshold frequency) increases:
(a) the maximum kinetic energy of electrons (b) the threshold frequency (c) the work function (d) the number of electrons emitted

Intensity controls the number of electrons; frequency controls their maximum energy. Answer: (d).

Q5. In a nuclear reactor, the moderator:
(a) absorbs neutrons (b) slows down neutrons (c) cools the core (d) shields radiation

Control rods absorb; the moderator slows. Answer: (b).

Q6. The energy equivalent of 1 g of mass is:
(a) 9 × 10¹⁶ J (b) 3 × 10⁸ J (c) 9 × 10¹³ J (d) 9 × 10¹⁰ J

E = mc² = 10⁻³ × 9 × 10¹⁶ = 9 × 10¹³ J. Option (a) is for 1 kg. Answer: (c).

Common mistakes

• Mixing penetrating and ionising power. Gamma penetrates most; alpha ionises most.
• Confusing moderator and control rods. The moderator slows neutrons; control rods absorb them.
• Saying brighter light gives faster photoelectrons. Only higher frequency does.
• Calling the Sun's energy fission. It is fusion.
• Thinking a beta particle comes from the electron shells. It is created in the nucleus.

Practice set

1. The neutron was discovered by: (a) Chadwick (b) J J Thomson (c) Rutherford (d) Bohr
2. Isotopes of an element differ in the number of: (a) protons (b) electrons (c) protons and electrons (d) neutrons
3. After three half-lives, the fraction of a radioactive sample remaining is: (a) 1/3 (b) 1/6 (c) 1/8 (d) 1/9
4. Control rods in a nuclear reactor are made of: (a) cadmium or boron (b) heavy water (c) graphite (d) uranium
5. X-rays were discovered by: (a) Becquerel (b) Röntgen (c) Curie (d) Einstein
6. The energy of the Sun comes mainly from: (a) fission (b) fusion (c) combustion (d) radioactive decay
7. Of these, the radiation with the longest wavelength is: (a) X-rays (b) ultraviolet (c) infrared (d) radio waves
8. To make an n-type semiconductor, silicon is doped with: (a) boron (b) aluminium (c) gallium (d) phosphorus

Answers:

1. (a). In 1932.
2. (d). The proton number is the same.
3. (c). (½)³.
4. (a). They absorb neutrons.
5. (b). In 1895.
6. (b). Hydrogen nuclei fuse into helium.
7. (d). Radio waves sit at the long-wavelength end.
8. (d). A pentavalent impurity gives extra electrons.

What to do next

• Draw the alpha–beta–gamma table from memory, including changes in Z and A.
• Solve eight half-life questions using whole numbers of half-lives.
• Write the reactor-parts table and the electromagnetic spectrum in order with one use each.
• Cross-check the atomic structure facts with atomic structure and the periodic table, then do a full pass of the physics revision sheet.