Nuclear Chemistry and Applications of Radioactivity

Ordinary chemistry rearranges electrons; nuclear chemistry rearranges the nucleus itself. Because nuclear binding energies are about a million times larger than bond energies, a gram of uranium can release as much energy as three tonnes of coal — and the same radiation that images a patient's thyroid will, in a large enough dose, destroy the tissue it passes through. This unit covers both sides of that bargain.

21.1 Natural and artificial radioactivity

Natural radioactivity was discovered by Henri Becquerel in 1896, when a uranium salt fogged a wrapped photographic plate; Marie and Pierre Curie isolated polonium and radium from pitchblende in 1898. Every nucleus with Z > 83 is naturally radioactive, and a few lighter ones (⁴⁰₁₉K, ¹⁴₆C) are as well.

Property	α-particle	β-particle	γ-ray
Nature	helium nucleus, ⁴₂He²⁺	fast electron, ⁰₋₁e	electromagnetic wave
Charge	+2	−1	0
Mass (u)	4	1/1837	0
Speed	≈ 0.1 c	up to 0.99 c	c
Deflection in a field	small, towards −ve plate	large, towards +ve plate	none
Ionising power	very high (10 000)	medium (100)	low (1)
Penetrating power	low — stopped by paper	medium — stopped by 3 mm Al	very high — needs thick lead

Emission changes the nucleus according to the group displacement law:

Emission	Change in mass number A	Change in atomic number Z	Example
α	−4	−2	²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
β	0	+1	²³⁴₉₀Th → ²³⁴₉₁Pa + ⁰₋₁e
γ	0	0	excited nucleus loses energy only

Artificial (induced) radioactivity was discovered by Irène Curie and Frédéric Joliot in 1934. Bombarding aluminium with α-particles gave a radioactive isotope of phosphorus that does not occur in nature:

²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n

³⁰₁₅P → ³⁰₁₄Si + ⁰₊₁e (positron, half-life 2.5 min)

Natural radioactivity	Artificial radioactivity
Shown by heavy nuclei, mostly Z > 83	can be induced in almost any element
Spontaneous; cannot be started or stopped	produced by bombardment in a reactor or accelerator
Emits α, β, γ	often emits positrons or neutrons as well
Half-lives usually long	usually short, which is why such isotopes are safer in medicine

21.2 Units of radioactivity

Quantity	SI unit	Older unit	Relation
Activity (disintegrations per second)	becquerel, Bq = 1 dps	curie, Ci	1 Ci = 3.7 × 10¹⁰ Bq
		rutherford, Rd	1 Rd = 10⁶ Bq
Absorbed dose (energy per kg of tissue)	gray, Gy = 1 J kg⁻¹	rad	1 rad = 0.01 Gy
Equivalent dose (absorbed dose × quality factor)	sievert, Sv	rem	1 rem = 0.01 Sv
Exposure (ionisation in air)	C kg⁻¹	roentgen, R	1 R = 2.58 × 10⁻⁴ C kg⁻¹

The curie was originally the activity of 1 g of radium-226. The quality factor Q is 1 for β and γ, but 20 for α-particles, because an α deposits its energy over a very short track and does far more damage per joule.

21.3 Nuclear reactions

A nuclear reaction is a change in the composition of a nucleus caused by bombardment with a particle. The first artificial transmutation was carried out by Rutherford in 1919:

¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H , written in short as ¹⁴N(α, p)¹⁷O

Chadwick's discovery of the neutron (1932) used the same technique:

⁹₄Be + ⁴₂He → ¹²₆C + ¹₀n

Chemical reaction	Nuclear reaction
Involves outer electrons only	involves the nucleus
Element identity is preserved	one element changes into another
Energy change 10–1000 kJ mol⁻¹	energy change ≈ 10⁹ kJ mol⁻¹
Rate depends on temperature, pressure, catalyst	independent of all of these
Mass is conserved	measurable mass is converted to energy

21.4 Nuclear fission and fusion reactions

Nuclear fission is the splitting of a heavy nucleus into two nuclei of comparable mass, with the release of neutrons and a large amount of energy:

²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + 200 MeV

Because each fission releases more neutrons than it consumes, a chain reaction is possible once the sample exceeds its critical mass (about 15 kg for pure ²³⁵U). Below that size too many neutrons escape from the surface.

Nuclear fusion is the joining of two light nuclei into a heavier one. It powers the Sun, where the overall change is

4 ¹₁H → ⁴₂He + 2 ⁰₊₁e + 26.7 MeV

and the reaction used in thermonuclear devices and in experimental reactors is

²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV

	Fission	Fusion
Nuclei	heavy (²³⁵U, ²³⁹Pu) split	light (²H, ³H) combine
Starting condition	a slow neutron	10⁷–10⁸ K ("thermonuclear")
Energy per reaction	≈ 200 MeV	≈ 17.6 MeV
Energy per nucleon	≈ 0.85 MeV	≈ 3.5 MeV — fusion is richer
Products	radioactive fission fragments	mostly non-radioactive helium
Control	achieved (reactors)	not yet achieved commercially

21.5 Nuclear power and nuclear weapons

In a nuclear reactor the chain reaction is held at exactly one new fission per fission — a controlled chain reaction — and the heat raises steam for a turbine.

Part	Material	Function
Fuel	UO₂ enriched to 3–4 % ²³⁵U, or ²³⁹Pu	undergoes fission
Moderator	graphite, heavy water D₂O, or ordinary water	slows fast neutrons so they can be captured by ²³⁵U
Control rods	boron steel or cadmium	absorb surplus neutrons; pushed in to slow the reactor down
Coolant	water, CO₂, liquid sodium	carries the heat to the boiler
Shield	thick concrete and lead	stops neutrons and γ-rays escaping

A nuclear weapon is the same reaction left uncontrolled: two sub-critical pieces of ²³⁵U or ²³⁹Pu are slammed together to exceed the critical mass, and the whole chain runs in about a microsecond. The bomb dropped on Hiroshima in 1945 used ²³⁵U and that on Nagasaki ²³⁹Pu. A hydrogen bomb uses a fission bomb only as a trigger, to reach the 10⁸ K needed for the fusion of deuterium and lithium deuteride, and is far more powerful.

Nepal has no nuclear power plant; its electricity is hydro. But radioisotopes are imported and used daily in Nepali hospitals and industry, which is why the Nepal Atomic Energy Act and a national regulatory framework exist.

21.6 Industrial uses of radioactivity

Use	Isotope	Principle
Thickness gauge for paper, plastic and steel sheet	⁸⁵Kr, ⁹⁰Sr (β)	transmitted intensity falls as thickness rises; the rollers adjust automatically
Level gauge in sealed tanks and cement silos	⁶⁰Co (γ)	γ-beam is blocked when material reaches the detector
Industrial radiography of welds and castings	⁶⁰Co, ¹⁹²Ir (γ)	cracks show as dark lines on film — a "γ X-ray" for steel
Leak detection in buried pipelines	²⁴Na (t½ = 15 h)	the tracer collects at the leak and is found with a counter at the surface
Engine wear and lubricant testing	⁵⁹Fe	activity of the oil measures metal worn off the piston rings
Food preservation and sterilisation of syringes	⁶⁰Co	γ-rays kill bacteria and insects without heating
Smoke detectors	²⁴¹Am (α)	smoke absorbs the α-particles and the ionisation current falls
Polymerisation and vulcanisation	⁶⁰Co	radiation starts free-radical cross-linking

21.7 Medical uses of radioactivity

Purpose	Isotope	Use
Thyroid imaging and treatment	¹³¹I (t½ 8 d)	iodine concentrates in the thyroid; small doses scan it, large doses destroy a tumour
General imaging (bone, heart, kidney)	⁹⁹ᵐTc (t½ 6 h)	pure γ-emitter, short-lived — the workhorse of nuclear medicine
PET scanning	¹⁸F (t½ 110 min)	as fluorodeoxyglucose, it shows where tissue is most active
Cancer radiotherapy (teletherapy)	⁶⁰Co (t½ 5.3 y)	a focused γ-beam kills dividing tumour cells
Brachytherapy (implants)	¹²⁵I, ¹⁹²Ir	the source is placed inside or beside the tumour
Blood volume, circulation studies	²⁴Na, ⁵¹Cr	tracer dilution
Sterilisation of sutures, syringes, dressings	⁶⁰Co	cold sterilisation of sealed packets
Bone-marrow and leukaemia therapy	³²P (β)	concentrates in rapidly dividing tissue

The isotopes chosen for diagnosis are γ-emitters with short half-lives, so that they leave the body quickly; those chosen for therapy are α- or β-emitters, whose short range concentrates the damage on the tumour.

21.8 Radiocarbon dating

Cosmic-ray neutrons in the upper atmosphere convert nitrogen into radioactive carbon-14:

¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁H

The ¹⁴C mixes into atmospheric CO₂ and enters every living thing through photosynthesis, so a living organism keeps a fixed ¹⁴C level giving about 15.3 disintegrations per minute per gram of carbon. At death the intake stops and the ¹⁴C decays with a half-life of 5730 years:

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Comparing the activity of a dead sample with that of living matter therefore gives its age. The method was developed by W. F. Libby (Nobel Prize 1960) and works up to about 50 000 years — beyond that too little ¹⁴C is left.

21.9 Harmful effects of nuclear radiations

Radiation damages tissue by ionising the molecules it passes through. The ions and free radicals formed (especially from water) break DNA strands and destroy enzymes.

Effect	Description
Somatic — in the exposed person	burns, hair loss, nausea and vomiting, fall in white cell count, sterility, cataract, leukaemia and other cancers years later
Genetic — in the descendants	mutation of the germ cells, causing inherited defects
Acute radiation sickness	a whole-body dose above about 1 Sv; above 5 Sv death is likely within weeks
Environmental	fallout isotopes ⁹⁰Sr (follows calcium into bone) and ¹³¹I (into the thyroid); waste that stays dangerous for thousands of years

Recommended limits are 1 mSv per year for the public and 20 mSv per year for radiation workers, against a natural background of about 2–3 mSv a year (much of it radon gas seeping from the ground). Protection rests on three things: distance (intensity falls as 1/r²), shielding (lead, concrete) and time (minimum exposure), with film badges or dosimeters worn to record the dose received.

Chapter summary

• Radioactivity is the spontaneous disintegration of an unstable nucleus; discovered by Becquerel (1896), it is unaffected by temperature, pressure or chemical combination.
• α = ⁴₂He (high ionising, low penetrating), β = ⁰₋₁e, γ = electromagnetic (low ionising, high penetrating). α emission: A − 4, Z − 2; β emission: A same, Z + 1.
• Artificial radioactivity (Joliot-Curie, 1934): ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n, and ³⁰₁₅P → ³⁰₁₄Si + ⁰₊₁e.
• Units: activity 1 Bq = 1 dps, 1 Ci = 3.7 × 10¹⁰ Bq; absorbed dose 1 Gy = 1 J kg⁻¹ = 100 rad; equivalent dose 1 Sv = 100 rem.
• In every nuclear equation the mass numbers and the atomic numbers must balance; the mass defect appears as energy, with 1 u = 931.5 MeV.
• Fission: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + 200 MeV, giving a chain reaction above the critical mass. Fusion: ²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV, needing 10⁷–10⁸ K.
• Reactor parts: fuel (3–4 % ²³⁵U), moderator (graphite or D₂O), control rods (boron or cadmium), coolant and concrete shield; a weapon is the same reaction uncontrolled.
• Industrial uses: thickness and level gauges, radiography of welds (⁶⁰Co, ¹⁹²Ir), leak detection (²⁴Na), sterilisation and food preservation, smoke detectors (²⁴¹Am). Medical uses: ⁹⁹ᵐTc imaging, ¹³¹I thyroid, ⁶⁰Co teletherapy, ³²P.
• Radiocarbon dating: ¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁H; living carbon gives 15.3 dpm g⁻¹; t½ = 5730 y; t = (2.303/λ) log(N₀/N).
• Radiation causes somatic and genetic damage; limits are 1 mSv yr⁻¹ (public) and 20 mSv yr⁻¹ (workers); protect by distance, shielding and time.

Practice questions

Group A — Multiple choice (1 mark each)

1. Which radiation has the greatest penetrating power? [1]aαbβcγdall are equal
2. When a nucleus emits an α-particle, its atomic number [1]aincreases by 1bdecreases by 2cdecreases by 4dis unchanged
3. 1 curie is equal to [1]a3.7 × 10¹⁰ Bqb10⁶ Bqc1 J kg⁻¹d100 rem
4. The moderator in a nuclear reactor is used to [1]aabsorb neutronsbslow down neutronsccool the coredenrich the fuel
5. The half-life of ¹⁴C used in radiocarbon dating is [1]a5730 daysb1600 yearsc5730 yearsd4.5 × 10⁹ years
6. The isotope most widely used for diagnostic imaging is [1]a⁶⁰Cob²³⁵Uc⁹⁹ᵐTcd²⁴¹Am

Answers to Group A

1. (c) — γ-rays are uncharged and massless, so they ionise little and travel far.

2. (b) — α emission removes 2 protons and 2 neutrons.

3. (a) — the activity of 1 g of radium-226.

4. (b) — slow (thermal) neutrons are captured by ²³⁵U far more readily.

5. (c) — 5730 years.

6. (c) — ⁹⁹ᵐTc is a short-lived pure γ-emitter.

Group B — Short answer (5 marks each)

1. Distinguish between natural and artificial radioactivity with one example of each. [5]
2. Compare α, β and γ radiations under nature, charge, ionising power and penetrating power. [5]
3. Define becquerel, curie, gray and sievert, and state the relations between the SI and the older units. [5]
4. What is nuclear fission? Write the equation for the fission of ²³⁵U and explain the terms chain reaction and critical mass. [5]
5. Give four industrial and four medical applications of radioactivity, naming the isotope used in each. [5]
6. A sample of charcoal from a cave gives 3.83 dpm per gram of carbon, while living wood gives 15.3. Calculate the age of the charcoal (t½ = 5730 years). [5]

Answers to Group B

1. Natural radioactivity is the spontaneous disintegration of heavy nuclei found in nature (²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He); artificial radioactivity is induced by bombarding a stable nucleus with particles (²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n, followed by ³⁰₁₅P → ³⁰₁₄Si + ⁰₊₁e). Natural activity occurs mostly for Z > 83 and has long half-lives; induced activity can be made in almost any element and is usually short-lived.

2. See the table in §21.1: α is ⁴₂He²⁺, charge +2, ionising power ≈ 10 000, stopped by paper; β is an electron, charge −1, ionising power ≈ 100, stopped by 3 mm of aluminium; γ is an electromagnetic wave, no charge, ionising power 1, needs thick lead.

3. Becquerel = one disintegration per second; curie = 3.7 × 10¹⁰ Bq; gray = absorbed dose of 1 J kg⁻¹ (1 rad = 0.01 Gy); sievert = absorbed dose × quality factor (1 rem = 0.01 Sv). For β and γ, Q = 1; for α, Q = 20.

4. Fission is the splitting of a heavy nucleus into two lighter nuclei with the release of neutrons and energy: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + 200 MeV. The three neutrons can cause three further fissions, so the process becomes self-sustaining — a chain reaction. The critical mass is the smallest mass of fissile material in which enough neutrons are retained (rather than escaping through the surface) for the chain to continue; for pure ²³⁵U it is about 15 kg.

5. Industrial: thickness gauges (⁸⁵Kr), radiography of welds (⁶⁰Co or ¹⁹²Ir), pipeline leak detection (²⁴Na), smoke detectors (²⁴¹Am). Medical: thyroid scan and therapy (¹³¹I), general imaging (⁹⁹ᵐTc), cancer teletherapy (⁶⁰Co), sterilisation of syringes (⁶⁰Co) or bone-marrow therapy (³²P).

6. 3.83/15.3 = 0.25, that is ¼ of the original activity = 2 half-lives. Age = 2 × 5730 = 11 460 years. By formula: λ = 0.693/5730 = 1.209 × 10⁻⁴ yr⁻¹; t = (2.303/1.209 × 10⁻⁴) log 4 = 1.905 × 10⁴ × 0.602 = 1.15 × 10⁴ years.

Group C — Long answer (8 marks each)

1. (a) What are nuclear fission and nuclear fusion? Write one equation for each and compare them under four headings. [4](b) Describe the parts of a nuclear reactor and the function of each, and explain why a reactor cannot explode like a bomb. [4]
2. (a) Explain the principle of radiocarbon dating and state its limitations. [4](b) Each fission of ²³⁵U releases 200 MeV. Calculate the energy released when 0.50 g of ²³⁵U undergoes complete fission. (1 MeV = 1.602 × 10⁻¹³ J) [4]

Answers to Group C

1. (a) Fission is the splitting of a heavy nucleus (²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n); fusion is the union of light nuclei (²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV). Compare on the nuclei involved, the starting condition (a slow neutron versus 10⁷–10⁸ K), energy per nucleon (0.85 versus 3.5 MeV) and products (radioactive fragments versus helium) — see the table in §21.4. (b) Fuel (UO₂, 3–4 % ²³⁵U) provides the fissile nuclei; the moderator (graphite or D₂O) slows the fast neutrons; control rods of boron or cadmium absorb surplus neutrons and hold the multiplication factor at 1; the coolant carries heat to the boiler; the concrete-and-lead shield stops radiation. It cannot explode like a bomb because the fuel is far too dilute in ²³⁵U and the core would blow itself apart long before a nuclear explosion could build up; the hazards are steam or hydrogen explosions and the escape of fission products.

2. (a) Cosmic-ray neutrons make ¹⁴C in the atmosphere (¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁H); it enters living matter as CO₂ and stays at a steady level of 15.3 dpm per gram of carbon. On death the intake stops and the ¹⁴C decays (¹⁴₆C → ¹⁴₇N + ⁰₋₁e, t½ = 5730 y), so the age follows from t = (2.303/λ) log(N₀/N). Limitations: only for once-living material; an upper limit of about 50 000 years; it assumes the atmospheric ¹⁴C level has been constant, which fossil-fuel burning and bomb tests have disturbed; and the sample must not be contaminated with modern carbon. (b) N = (0.50/235) × 6.022 × 10²³ = 1.28 × 10²¹ nuclei. Energy = 1.28 × 10²¹ × 200 = 2.56 × 10²³ MeV = 2.56 × 10²³ × 1.602 × 10⁻¹³ = 4.1 × 10¹⁰ J (4.1 × 10⁷ kJ).