Nuclear Chemistry Notes

Nuclear Structure

The atomic nucleus is at the center of an atom.
The nucleus contains protons and neutrons, which are collectively referred to as nucleons.
Protons are positively charged particles.
Neutrons have no electric charge and have a mass slightly larger than that of a proton; they were discovered in 1932 by James Chadwick.
Evidence for protons was discovered in 1886 by Eugene Goldstein.

Strong Nuclear Force

The electric repulsion between protons strains the nucleus.
The gravitational force is too weak to counteract the repulsive electric force between protons.
The strong nuclear force holds the nucleus together, counteracting the electric repulsion.

Nuclear Symbol of an Atom

$A = Z + N$ where:
- $A$ = Mass number (number of protons and neutrons, also called nucleon number).
- $Z$ = Atomic number = number of protons.
- $N$ = Neutron number.
$X$ = Chemical symbol for the element.
Example for Carbon-12:
- $^{12}_6C$
- $A = 12$
- $Z = 6$
- $N = 6$

Atomic Number and Mass Number

The number of protons (atomic number, $Z$ ) differs for different elements.
In a neutral atom, the number of protons equals the number of electrons.
The number of neutrons is denoted as $N$ .
The atomic mass number $A$ is approximately equal to the mass of a single nucleon times $A$ .

Particle Properties

Electron:
- Electric Charge: $-1.60 × 10^{-19} C$
- Atomic Mass Units: $5.485 799 × 10^{-4} u$
Proton:
- Electric Charge: $+1.60 × 10^{-19} C$
- Atomic Mass Units: $1.007 276 u$
Neutron:
- Electric Charge: $0$
- Atomic Mass Units: $1.008 665 u$
Hydrogen Atom:
- Electric Charge: $0$
- Atomic Mass Units: $1.007 825 u$

Nuclear Symbols for Particles

Proton: $\begin{matrix} ^1_1H \end{matrix}$
Neutron: $\begin{matrix} ^1_0n \end{matrix}$
Electron: $\begin{matrix} ^0_{-1}e \end{matrix}$
- $A = 0$ because electrons are not composed of protons or neutrons.
- $Z = -1$ because the electron has a negative charge.

Isotopes

Isotopes are nuclei with the same number of protons but different numbers of neutrons.
Notation: $^{A}_{Z}X$

Atomic Mass Calculation

The average atomic mass is calculated by multiplying the mass of each isotope by its decimal abundance and summing the results.
The average atomic mass of carbon is approximately 12.011 amu.

Nuclear Stability

For a nucleus to be stable, the electrostatic repulsion between protons must be balanced by the strong nuclear force.
As the number of protons ( $Z$ ) increases, the number of neutrons ( $N$ ) must increase even more to maintain stability.
There is a point where a balance of repulsive and attractive forces cannot be achieved by increasing the number of neutrons.

Stable Nuclei

Stable nuclei generally have more neutrons than protons as the atomic number increases.
The stable nucleus with the largest number of protons ( $Z = 83$ ) is bismuth, which contains 126 neutrons.
Nuclei with more than 83 protons (e.g., uranium, $Z = 92$ ) are unstable and undergo spontaneous disintegration or rearrangement (radioactivity).
Radioactivity was first discovered in 1896 by Antoine Becquerel.

Alpha Decay

Alpha decay involves the emission of an alpha particle, which consists of 2 protons and 2 neutrons (identical to a helium-4 nucleus).
When an atom undergoes alpha decay:
- The mass number ( $A$ ) decreases by 4.
- The atomic number ( $Z$ ) decreases by 2.
This process reduces the size and energy of the unstable nucleus, making it more stable.
Example: Uranium-238 decaying into Thorium-234:

Characteristics of Alpha Decay

Low penetration: Stopped by paper or skin.
Highly ionizing: Can cause significant damage to nearby biological tissue.
Common in heavy elements (like uranium, radium, plutonium).

Beta Decay

Beta decay is a type of radioactive decay where an unstable nucleus changes a neutron into a proton or vice versa, emitting a beta particle and a neutrino or antineutrino.
A neutrino is a subatomic particle with no electric charge and a very small mass.

Types of Beta Decay

Beta-minus
- A neutron turns into a proton.
- Emits a beta particle (electron) and antineutrino.
- Atomic number increases by 1, mass number unchanged.
Beta-plus ( $\beta^{+}$ ) decay (positron emission):
- A proton turns into a neutron.
- Emits a positron and neutrino.
- Atomic number decreases by 1, mass number unchanged.

Characteristics of Beta Decay

Beta particles are more penetrating than alpha particles but less ionizing.
Beta decay follows conservation of charge and mass number.
It's a result of the weak nuclear force.

Gamma Decay

Gamma decay is a type of radioactive decay where an excited nucleus releases excess energy by emitting a gamma ray (high-energy photon).

What Happens in Gamma Decay?

After alpha or beta decay, the daughter nucleus is often left in an excited state.
It becomes more stable by emitting a gamma photon ( $\gamma$ ).
No particles are lost, so:
- Atomic number stays the same
- Mass number stays the same

Characteristics of Gamma Decay

Gamma rays are electromagnetic waves, not particles.
Very high penetration—can pass through body tissue and even thick lead.
Low ionizing ability compared to alpha and beta radiation.
Often accompanies alpha or beta decay but can occur on its own.

Summary Comparison of Decay Types

Decay Type	Emitted	Mass Change	Atomic # Change	Penetration	Ionizing
Alpha	α (He nucleus)	-4	-2	Low	High
Beta	β⁻ or β⁺	None	±1	Medium	Medium
Gamma	γ (photon)	None	None	High	Low

Half-Life

Half-life is the time it takes for half of the atoms in a radioactive substance to decay into a more stable form.
After one half-life: 50% of the original radioactive atoms remain.
After two half-lives: 25% remain (half of the 50%).
This continues, where n = number of half-lives.
Example: Carbon-14 has a half-life of 5,730 years:
- After 5,730 years → 50% remains.
- After 11,460 years → 25% remains.
- After 17,190 years → 12.5% remains.
To calculate the amount remaining:
- $N_0$ : original quantity
- $t$ : time elapsed
- $T_{1/2}$ : half-life
- $N(t)$ : quantity remaining after time t

Sample Problem: Uranium-238 Dating

Uranium-238 has a half-life of 4.5 billion years. If you start with a 200 g sample, how much remains after 13.5 billion years?

Decay Series

A decay series (or radioactive decay chain) is a sequence of radioactive decays where an unstable parent isotope undergoes multiple steps of decay until it becomes a stable daughter isotope.
- Alpha decay ( $\alpha$ ) – loss of 2 protons and 2 neutrons
- Beta decay ( $\beta$ ) – a neutron converts into a proton (or vice versa)
Example: Uranium-238 → Lead-206:
1. $U-238 → Th-234$ ( $\alpha$ decay)
2. $Th-234 → Pa-234$ ( $\beta^{-}$ decay)
3. $Pa-234 → U-234$ ( $\beta^{-}$ decay)
4. $U-234 → Th-230$ ( $\alpha$ decay)
5. Continues through Ra, Rn, Po, Bi, etc.
6. Final: $Pb-206$ (stable)
Total: 14 steps including multiple $\alpha$ and $\beta$ decays.

Why Are Decay Series Important?

Help date ancient rocks and fossils.
Essential in nuclear power and radiation safety.
Explain natural background radiation.
Some intermediates (like radon gas) pose health risks.

Nuclear Fission

Nuclear fission is the process by which a heavy nucleus splits into smaller nuclei, releasing energy.
Energy \ Release = Neutron + Fissile \ Nucleus \ (Uranium-235) -> Split \ U-235 \ releases \ heat, \ neutrons, \ gamma \ radiation \ and \ fission \ products -> Released \ neutrons \ chain \ reaction

Products of Nuclear Fission

Two (or more) smaller nuclei – called fission fragments.
- The specific elements vary but are always lighter than the original heavy nucleus.
Free neutrons
- Usually 2 or 3 neutrons are released per fission event.
- These neutrons can trigger further fission reactions, leading to a chain reaction.
Energy
- Released mostly as kinetic energy of the fragments and neutrons.
- Some is also released as gamma radiation and heat.
Gamma radiation
- High-energy electromagnetic waves emitted by the unstable fission fragments as they decay into more stable forms.

Nuclear Fusion

Nuclear fusion is the process in which two light atomic nuclei combine to form a heavier nucleus, releasing a tremendous amount of energy.
It's the opposite of nuclear fission.
Example Reaction (in stars like our Sun):
- A small amount of mass is converted into energy according to Einstein’s equation: $E = mc^2$

Conditions Needed for Nuclear Fusion

Very high temperature (millions of degrees)
High pressure to overcome electrostatic repulsion between nuclei

Advantages over Fission

Produces more energy than fission
No long-lived radioactive waste
Fuel (hydrogen) is abundant

Challenges of Nuclear Fusion

Extremely difficult to achieve and sustain on Earth
Requires more energy to start the reaction than it currently produces (in most labs)

Fusion in Real Life

Stars: The Sun fuses hydrogen into helium, producing light and heat.
Experimental Reactors: Projects like ITER (International Thermonuclear Experimental Reactor) are trying to make fusion practical on Earth.

Symbols Used in Nuclear Chemistry

Name	Notation	Symbol
Alpha particle	$\begin{matrix} ^4_2He \end{matrix}$ or α	α
Beta particle	$\begin{matrix} ^0_{-1}e \end{matrix}$ or β	β⁻
Gamma radiation	γ	γ
Neutron	$\begin{matrix} ^1_0n \end{matrix}$	n
Proton	$\begin{matrix} ^1_1H \end{matrix}$ or p	p
Positron	$\begin{matrix} ^0_{+1}e \end{matrix}$ or β	β⁺

Worksheet Problems

(A series of nuclear chemistry worksheet problems covered in the lecture.)