Chemistry Regents

1. Why nuclear chemistry is different

Every reaction in Topics 1 through 9 was a chemical reaction. Atoms kept their identity. Sodium stayed sodium. Carbon stayed carbon. What changed was how electrons were shared or transferred. A nuclear reaction is fundamentally different: the nucleus itself changes, and one element turns into a different element.

Chemical vs nuclear: the four contrasts

What changes Chemical: electrons. Nuclear: protons and neutrons in the nucleus.

Element identity Chemical: preserved. Nuclear: changes (one element becomes another).

Energy released Chemical: tens to hundreds of kJ/mol. Nuclear: millions of kJ/mol.

Affected by conditions Chemical: yes (temperature, pressure, catalysts). Nuclear: no. A radioactive sample decays at the same rate in a freezer or a furnace.

That last point is worth slowing down on. You spent all of Topic 6 learning how to push equilibrium and speed up rates with heat, pressure, and catalysts. None of that touches a nucleus. Half-life is a fixed property of an isotope. You cannot speed up uranium decay by heating it, and you cannot slow it down by cooling it.

2. The five decay particles (Table O)

Table O on your reference sheet lists exactly five particles you need to know. Memorize the symbol, mass number, and atomic number of each. Every nuclear equation on the Regents uses one of these.

Name	Symbol	Mass number (top)	Atomic number (bottom)	What it actually is
Alpha particle	⁴₂α or ⁴₂He	4	+2	A helium-4 nucleus. Two protons, two neutrons.
Beta particle	⁰_-1β or ⁰_-1e	0	-1	A high-speed electron emitted from the nucleus when a neutron converts to a proton.
Positron	⁰₊₁β or ⁰₊₁e	0	+1	The antimatter twin of an electron. Same mass, opposite charge.
Gamma ray	⁰₀γ	0	0	High-energy electromagnetic radiation. No mass, no charge. Often released alongside other decay.
Neutron	¹₀n	1	0	A free neutron. Appears in fission and in artificial transmutation.

Reading the notation

Every nuclear symbol has the same layout: the top number is mass (protons plus neutrons), and the bottom number is charge or atomic number (protons, for atoms). For a beta particle, the bottom -1 is its charge, not an atomic number. It still counts as -1 when you balance the equation. That single convention makes balancing equations trivial once you trust it.

Penetrating power, in case it shows up

Alpha is the heaviest and slowest, stopped by paper or skin. Beta is lighter and faster, stopped by aluminum foil or a few mm of plastic. Gamma has no mass and travels at the speed of light, requiring thick lead or concrete to stop. This is occasionally asked. The order from least to most penetrating is alpha < beta < gamma.

3. The five types of decay

Decay is what happens when an unstable nucleus throws off a particle to become more stable. Each type of decay changes the parent atom in a predictable way. Learn what each type does to mass number and atomic number, and you can finish any decay equation in your head.

Alpha decay

A heavy nucleus emits an alpha particle (⁴₂He). The parent loses 4 from mass number and 2 from atomic number.

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Beta decay

A neutron in the nucleus converts to a proton, ejecting a high-speed electron (the beta particle). The mass number stays the same, but atomic number goes up by 1 because a neutron just became a proton.

¹⁴₆C → ¹⁴₇N + ⁰_-1e

Positron emission

The opposite of beta decay. A proton converts to a neutron and ejects a positron. Mass number stays the same, but atomic number goes down by 1.

³⁷₁₉K → ³⁷₁₈Ar + ⁰₊₁e

Gamma emission

Pure energy comes out as a gamma ray. Nothing changes about the parent atom, mass number or atomic number. The nucleus simply drops to a lower energy state. Gamma rays are usually emitted alongside another type of decay, not on their own.

Electron capture (less commonly tested)

A proton in the nucleus pulls in an inner-shell electron and becomes a neutron. Result: same mass number, atomic number down by 1. The effect is identical to positron emission.

Decay cheat sheet

Type of decay	Effect on mass number	Effect on atomic number
Alpha (⁴₂He)	-4	-2
Beta (⁰_-1e)	0	+1
Positron (⁰₊₁e)	0	-1
Gamma (⁰₀γ)	0	0
Electron capture	0	-1

4. Natural vs artificial transmutation

Transmutation is the umbrella term for any change in the identity of a nucleus, that is, any reaction that changes the atomic number. The Regents distinguishes two flavors.

Natural transmutation Happens spontaneously. One reactant, namely the unstable parent isotope. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.

Artificial transmutation Caused by humans bombarding a nucleus with a high-energy particle (often a neutron, alpha, or proton). Two reactants on the left side. Example: ²⁷₁₃Al + ⁴₂He → ³⁰₁₅P + ¹₀n.

The one-reactant rule

The fastest way to tell them apart on a multiple-choice question: count the reactants. One reactant means natural. Two reactants means artificial. That single test answers nearly every transmutation question on the exam.

5. Balancing nuclear equations

Two conservation laws. That is the whole game.

The two conservation laws

Mass numbers (the top numbers) must sum to the same total on both sides.
Atomic numbers (the bottom numbers) must sum to the same total on both sides.

If you know four of the five values in an equation, you can always find the missing one by arithmetic, then look up the resulting atomic number on the periodic table to identify the element.

Worked example: find the missing product

Complete the equation: ²²⁶₈₈Ra → ___ + ⁴₂He

Mass numbers: 226 = ? + 4, so ? = 222.
Atomic numbers: 88 = ? + 2, so ? = 86.
Identify element: Atomic number 86 is radon (Rn).
Answer: ²²²₈₆Rn.

Worked example: identify the type of decay

In the reaction ³²₁₅P → ³²₁₆S + ?, what is the emitted particle?

Mass numbers: 32 = 32 + ?, so ? = 0.
Atomic numbers: 15 = 16 + ?, so ? = -1.
Identify particle: mass 0, charge -1 is a beta particle, ⁰_-1e.
Answer: beta decay.

Sign warning

Beta particles have charge -1, positrons have charge +1. When you do the arithmetic, remember that subtracting a negative is the same as adding. The most common Regents trick is to put a beta particle on the right side and expect you to notice the atomic number rises by 1 on the parent side.

6. Half-life and Table N

Half-life is the time it takes for half the atoms in a radioactive sample to decay. It is a fixed property of each isotope. Table N on your reference sheet gives the half-life of every isotope you need to know, plus its mode of decay and a typical use.

Selected entries from Table N

Isotope	Half-life	Decay mode	Common use
Carbon-14	5,715 years	Beta	Dating organic remains
Iodine-131	8.021 days	Beta	Thyroid imaging and treatment
Cobalt-60	5.271 years	Beta and gamma	Cancer radiation therapy
Uranium-235	7.04 × 10⁸ years	Alpha	Fission fuel in power reactors
Uranium-238	4.47 × 10⁹ years	Alpha	Geologic (rock) dating
Potassium-40	1.26 × 10⁹ years	Beta	Geologic dating

The half-life formula in plain English

After one half-life, half is left. After two, a quarter. After three, an eighth. The pattern is (1/2)ⁿ, where n is the number of half-lives that have passed.

The four quantities, always

Every half-life problem is built from the same four quantities. If you know three, you can find the fourth.

Original mass (or starting amount)
Remaining mass (or fraction left)
Half-life (from Table N)
Total time elapsed

Quick relationship: number of half-lives n = (total time) ÷ (half-life), and the fraction remaining = (1/2)ⁿ.

Worked example: how much is left

A sample contains 80.0 g of I-131. How many grams remain after 24.063 days?

Half-life of I-131 is 8.021 days (Table N).
Number of half-lives: 24.063 ÷ 8.021 = 3.
Fraction remaining: (1/2)³ = 1/8.
Mass remaining: 80.0 g × (1/8) = 10.0 g.

Worked example: how old is the sample

A wooden artifact has 1/4 of its original C-14 still present. How old is it?

Half-life of C-14 is 5,715 years.
1/4 remaining means 2 half-lives have passed.
Age = 2 × 5,715 years = 11,430 years.

Worked example: working backward to find half-life

A 100. g sample decays to 25 g in 30. minutes. What is its half-life?

100 g → 25 g is a factor of 1/4, which means 2 half-lives.
30 minutes ÷ 2 = 15 minutes per half-life.

Regents tip

Never multiply the original mass by (1/2)^{total time}. Always divide total time by the half-life first to get n, then raise (1/2) to that power. Mixing those two steps is the most common error on this topic.

7. Fission and fusion

Both fission and fusion release enormous amounts of energy by changing the nucleus. They are opposite processes, and the Regents loves to ask you to compare them.

Fission A heavy nucleus splits into two lighter nuclei when struck by a neutron. Produces extra neutrons that can trigger a chain reaction. Used in nuclear power plants and atomic bombs. Example: U-235 + n → Ba-141 + Kr-92 + 3n + energy.

Fusion Two light nuclei combine into a heavier nucleus. Requires extremely high temperatures (millions of degrees) to overcome proton-proton repulsion. Powers the sun. Example: ²₁H + ³₁H → ⁴₂He + ¹₀n + energy.

Feature	Fission	Fusion
Reactant size	One heavy nucleus (e.g. U-235)	Two light nuclei (e.g. H-2 and H-3)
Process	Nucleus splits apart	Nuclei combine
Conditions required	A neutron to initiate	Extreme temperature and pressure
Where it happens	Nuclear power plants, atomic bombs	The sun, stars, hydrogen bombs
Energy per reaction	Large	Larger (per gram of fuel)
Radioactive waste	Yes (long-lived fission products)	Much less

Two-word memory hooks

Fission = splitting. Picture a uranium nucleus shattering like a glass dropped on a tile floor.
Fusion = joining. Picture two hydrogen nuclei smashing together inside the sun.
Both release energy because the products are slightly less massive than the reactants. That missing mass became energy (E = mc²). You do not need to do the math, but you should know mass is converted to energy in both processes.

8. Uses and risks of radioisotopes

The Regents asks you to match a radioisotope to its application, and to discuss the benefits and dangers of nuclear technology in extended response questions. Table N gives you the isotope-use pairs. Here is the full picture.

Beneficial uses

Medical imaging I-131 traces and treats thyroid disease. Tc-99 is used in tumor imaging. Short half-lives mean the isotope decays away quickly and exposure is limited.

Cancer treatment Co-60 emits gamma rays that destroy cancer cells. Aimed precisely from outside the body.

Carbon-14 dating C-14 dates organic remains up to about 50,000 years old. Used in archaeology, paleontology, art authentication.

Geologic dating U-238 (half-life 4.47 × 10⁹ years) and K-40 (1.26 × 10⁹ years) date rocks and the age of the Earth itself.

Power generation U-235 fission in nuclear reactors produces electricity with no CO₂ emissions.

Food irradiation and tracers Gamma irradiation kills bacteria in food. Radioactive tracers track chemical pathways in living organisms.

Risks

Biological damage Ionizing radiation breaks chemical bonds in DNA, causing mutations, cancer, and tissue damage. Higher doses cause more damage.

Long-lived waste Some fission products have half-lives of thousands or millions of years. Storage is a long-term political and engineering problem.

Accident risk Reactor accidents (Chernobyl, Fukushima) can release radioactive material across large areas.

Weapons proliferation Fissile material used for power generation can be diverted to weapons.

Why short half-lives are good for medicine

Medical isotopes need to image or treat the patient and then decay away quickly. I-131 with its 8-day half-life is gone from the body in weeks. Tc-99m has a 6-hour half-life, ideal for a single-day diagnostic scan. You would not use U-235 as a medical tracer; it would still be radioactive billions of years after the patient died.

Key terms

Radioisotope	An isotope with an unstable nucleus that decays by emitting particles or energy.
Transmutation	Any nuclear reaction in which one element is converted into another. Natural has one reactant; artificial has two.
Alpha particle	A helium-4 nucleus (⁴₂He). Heaviest decay particle, least penetrating.
Beta particle	A high-speed electron (⁰_-1e) emitted when a neutron converts to a proton.
Positron	The antimatter counterpart of an electron (⁰₊₁e). Same mass, opposite charge.
Gamma ray	High-energy electromagnetic radiation. No mass, no charge, most penetrating.
Half-life	The time required for half the atoms in a radioactive sample to decay. A fixed property of each isotope.
Fission	The splitting of a heavy nucleus into two lighter nuclei, releasing energy and neutrons.
Fusion	The combining of two light nuclei into a heavier nucleus. Powers the sun.
Chain reaction	A self-sustaining series of fission events in which neutrons released by one fission trigger more fissions.
Ionizing radiation	Radiation energetic enough to remove electrons from atoms, damaging biological tissue.

Practice questions

Two multiple choice, one short answer, two extended response. The last one is the kind of question Regents Part C builds around: compare and contrast plus a real-world judgment.

Q1 (Multiple choice). In the reaction ²³⁹₉₃Np → ²³⁹₉₄Pu + X, the particle represented by X is

Answer: a beta particle, ⁰_-1e.

Mass numbers: 239 = 239 + ?, so ? = 0. Atomic numbers: 93 = 94 + ?, so ? = -1. A particle with mass 0 and charge -1 is a beta particle. Confirms what you would expect: the atomic number went up by 1, which is the signature of beta decay.

Q2 (Multiple choice). Which statement best describes both fission and fusion reactions?

Answer: Both processes release large amounts of energy by converting a small amount of mass into energy.

Fission splits heavy nuclei; fusion combines light ones. Opposite in mechanism, but both release energy because the products have slightly less total mass than the reactants. That mass difference is converted to energy. Distractors typically claim both produce hazardous waste in similar amounts, or that both require high temperatures. Fission only requires a neutron; fusion requires extreme temperature. Waste is much greater for fission.

Q3 (Multiple choice). A 16.0 g sample of an isotope decays to 2.00 g after 36.0 hours. What is the half-life of the isotope?

Answer: 12.0 hours.

16.0 g → 2.00 g is a factor of 1/8, which means 3 half-lives have passed. 36.0 hours ÷ 3 = 12.0 hours per half-life.

The trap answer is 18.0 hours, which comes from assuming 2 half-lives (1/4 remaining) instead of 3 (1/8 remaining). Slow down and count: 16 → 8 → 4 → 2. That is three halvings.

Q4 (Part B-2 short response, 2 points). A sample of K-42 has an initial mass of 60.0 g. The half-life of K-42 is 12.4 hours. Calculate the mass of K-42 remaining after 49.6 hours. Show all work.

Sample full-credit response:

Number of half-lives = 49.6 hours ÷ 12.4 hours = 4 half-lives.

Fraction remaining = (1/2)⁴ = 1/16.

Mass remaining = 60.0 g × (1/16) = 3.75 g.

Scoring: 1 point for correct setup (number of half-lives and the (1/2)ⁿ relationship), 1 point for the correct numerical answer with units.

Q5 (Part C extended response, 4 points). Co-60 is used in cancer treatment. (a) State the type of decay emitted by Co-60 according to Table N. (b) Explain why the long half-life of U-235 makes it suitable for use as a fuel in nuclear reactors but unsuitable for use as a medical tracer in the human body. (c) Discuss one risk and one benefit of using nuclear fission to generate electricity.

Sample full-credit response:

(a) According to Table N, Co-60 decays by emitting both beta particles and gamma rays. The gamma radiation is what is used to destroy cancerous tissue, since gamma rays are highly penetrating and can reach tumors located inside the body.

(b) U-235 has a half-life of about 7 × 10⁸ years. This is useful for fuel because the sample stays radioactive long enough to release energy continuously over the lifetime of a reactor. The same property makes it unsuitable as a medical tracer: an isotope inside the human body must decay away quickly so the patient is not exposed to radiation for years or decades. A medical isotope like I-131 has a half-life of about 8 days, so it leaves the body in a matter of weeks. U-235 would remain inside the patient essentially forever, continuously damaging tissue.

(c) One benefit of nuclear fission is that it generates large amounts of electricity without releasing carbon dioxide or other greenhouse gases, which makes it attractive as a low-carbon alternative to fossil fuels. One risk is that the fission products are radioactive and have very long half-lives, so the waste produced by reactors remains hazardous for thousands of years and must be stored securely. Accidents like Chernobyl and Fukushima also show that reactor failure can release radioactive material over large areas.

Scoring: 1 point for correctly stating the decay type from Table N. 1 point for explaining that long half-life means long-lasting radiation, with contrast between fuel use and medical use. 1 point for a valid benefit of fission. 1 point for a valid risk of fission.