Nuclear & Radioactivity — Set 3

Correct Answer: A. Equal to 1

• **Equal to 1** = When k = 1, each fission event produces exactly one neutron that causes another fission, maintaining a steady, self-sustaining chain reaction — this is the 'critical' condition. • **k < 1 subcritical; k > 1 supercritical** — A controlled nuclear reactor operates at k = 1; k > 1 means the reaction grows exponentially (bomb); k < 1 means the reaction dies out. • 💡 Wrong-option analysis: Exactly 0: k = 0 means no fission neutrons continue the reaction — the chain reaction stops completely (subcritical); Less than 0: a negative multiplication factor has no physical meaning in neutron chain reactions; Greater than 10: k > 10 would represent an uncontrolled runaway explosion, not a critical (steady) reactor.

Correct Answer: D. Slow down fast neutrons

• **Slow down fast neutrons** = The moderator (graphite, heavy water, or light water) slows fast fission neutrons to thermal energies (~0.025 eV), dramatically increasing the probability of causing further fissions in U-235. • **Thermal neutrons ≈ 0.025 eV** — Fast neutrons (MeV range) have a much lower fission cross-section for U-235; slowing them to thermal energies increases the cross-section by a factor of ~1000. • 💡 Wrong-option analysis: Convert gamma rays into alpha particles: no material converts gamma rays into alpha particles — these are completely different types of radiation; Stop all neutrons completely: stopping all neutrons would kill the chain reaction; that is the role of shut-down rods; Increase neutron speed greatly: increasing neutron speed would reduce fission probability in U-235-fuelled reactors, doing the opposite of what is needed.

Correct Answer: B. Absorb excess neutrons

• **Absorb excess neutrons** = Control rods made of boron, cadmium, or hafnium absorb neutrons strongly, reducing the neutron flux and allowing reactor power to be adjusted or the reactor to be shut down safely. • **⁶Li, ¹⁰B, ¹¹³Cd** — Cadmium-113 has one of the highest thermal neutron absorption cross-sections (~20,000 barns); inserting rods reduces k toward or below 1. • 💡 Wrong-option analysis: Produce more fuel: control rods do not produce fuel — they absorb neutrons; fuel breeding happens in specific blanket materials in breeder reactors; Increase temperature rapidly: absorbing neutrons with control rods reduces the chain reaction and lowers temperature — the opposite of increasing it; Convert uranium into oxygen: uranium cannot be chemically converted to oxygen by any reactor component — this is physically impossible.

Correct Answer: A. Remove heat from the reactor core

• **Remove heat from the reactor core** = The coolant (water, heavy water, CO₂, liquid sodium) circulates through the reactor core, absorbing the heat generated by fission and carrying it to steam generators to produce electricity. • **Efficiency ~33–40%** — The heat extracted drives turbines; without a coolant the core temperature would rise uncontrollably; coolant choice affects reactor design, safety, and efficiency. • 💡 Wrong-option analysis: Make fuel radioactive: the fuel (uranium or plutonium) is already radioactive before the coolant arrives; the coolant does not cause this; Stop fission completely: stopping fission is the role of control rods, not the coolant; Create gamma rays: gamma rays are produced by fission products, not by the coolant itself.

Correct Answer: B. Separate a nucleus into its nucleons

• **Separate a nucleus into its nucleons** = Nuclear binding energy is the minimum energy needed to completely disassemble a nucleus into its individual free protons and neutrons; equivalently, it is the energy released when nucleons combine to form the nucleus. • **B.E. per nucleon ≈ 8.8 MeV for Fe-56** — Iron-56 has the highest binding energy per nucleon of all stable nuclei, making it the most tightly bound nucleus; nuclei lighter or heavier than iron can release energy by fusion or fission respectively. • 💡 Wrong-option analysis: Create electrons in a wire: creating free electrons in a conductor requires ionisation energy or work function considerations — unrelated to nuclear binding; Start a chemical reaction: chemical reactions involve electron-level energy changes (~eV), millions of times smaller than nuclear binding energies (~MeV); Change temperature of a liquid only: heating a liquid involves thermal energy transfer, which is entirely different from nuclear binding energy.

Correct Answer: A. Speed of light in vacuum

• **Speed of light in vacuum** = In Einstein's mass-energy equivalence E = mc², c is the speed of light in vacuum, approximately 3 × 10⁸ m/s; this equation shows that mass and energy are interconvertible. • **c ≈ 3 × 10⁸ m/s** — Because c² ≈ 9 × 10¹⁶ J/kg, even a tiny mass converts to an enormous amount of energy; 1 kg of mass is equivalent to 9 × 10¹⁶ J. • 💡 Wrong-option analysis: Current in a circuit: electric current is denoted by I (amperes) in circuit equations, not c; Speed of sound: the speed of sound in air is ≈340 m/s — about one million times smaller than c; Charge of electron: the electron's charge is denoted e ≈ 1.6 × 10⁻¹⁹ C, not c.

Correct Answer: B. 1 volt

• **1 volt** = One electron-volt is the kinetic energy gained by a particle carrying one elementary charge when accelerated through a potential difference of exactly 1 volt; 1 eV = 1.6 × 10⁻¹⁹ J. • **1 eV = 1.6 × 10⁻¹⁹ J** — Atomic and nuclear energies are conveniently expressed in eV, keV, or MeV; for comparison, chemical bond energies are a few eV while nuclear binding energies are millions of eV (MeV). • 💡 Wrong-option analysis: 1 tesla: the tesla is the SI unit of magnetic flux density (B field), not a unit of potential; 1 ampere: the ampere is the SI unit of electric current — current × time = charge, not energy; 1 ohm: the ohm is the SI unit of electrical resistance — unrelated to the energy unit eV.

Correct Answer: D. 931 MeV

• **931 MeV** = Using E = mc², 1 u = 1.66054 × 10⁻²⁷ kg converts to approximately 931.5 MeV of energy; this is a fundamental constant in nuclear physics calculations. • **1 u = 931.5 MeV/c²** — The mass defect in nuclear reactions is typically a few thousandths of u, so binding energies are in the range of a few MeV; for iron-56, total binding energy ≈ 8.8 × 56 ≈ 490 MeV. • 💡 Wrong-option analysis: 9.31 MeV: this is 100 times too small — a common decimal-place error (931 ÷ 100); 9310 MeV: this is 10 times too large — another factor-of-10 error; 93.1 MeV: this is 10 times too small — yet another order-of-magnitude mistake.

Correct Answer: C. Strong and short-range

• **Strong and short-range** = The nuclear (strong) force is the strongest of the four fundamental forces, but it acts only over very short distances (∼1–3 fm = 10⁻¹⁵ m), dropping to negligible strength beyond about 3 fm. • **Range ≈ 1–3 fm** — At distances less than ∼0.5 fm it becomes repulsive (preventing nuclear collapse); between ∼0.8 and 3 fm it is strongly attractive, overcoming proton–proton electromagnetic repulsion. • 💡 Wrong-option analysis: Always repulsive only: the nuclear force is attractive over most of its range — it is only repulsive at very short distances (< 0.5 fm) to prevent nucleons from merging; Same as gravitational force: gravity is the weakest force and has infinite range — the nuclear force is roughly 10³⁸ times stronger but short-range; Weak and infinite-range: weak and infinite-range describes electromagnetism (not weak force) — the nuclear force is strong and short-range.

Correct Answer: B. James Chadwick

• **James Chadwick** = James Chadwick discovered the neutron in 1932 by bombarding beryllium with alpha particles and correctly interpreting the resulting neutral, penetrating radiation as a new uncharged particle. • **1932, Nobel Prize 1935** — Chadwick deduced the neutron's mass (~1.0087 u) from collision experiments; the discovery completed the modern picture of the nucleus as containing only protons and neutrons. • 💡 Wrong-option analysis: J. J. Thomson: Thomson discovered the electron in 1897 — a very different particle; Niels Bohr: Bohr developed the atomic model with quantised electron orbits (1913) — he did not discover the neutron; Ernest Rutherford: Rutherford discovered the proton (1919) and the nucleus (1911), but it was his colleague Chadwick who identified the neutron.