Radioactive decay - waves and particles Revision Notes

Atomic Nucleus Composition

The atomic nucleus, located at the center of an atom, is made up of subatomic particles called protons and neutrons. These particles are collectively known as nucleons. The nucleus is extremely dense and contains almost all of the atom's mass, despite being a tiny fraction of its overall volume.

Protons and Their Charge

Protons are one of the two types of particles found in the nucleus. Each proton carries a single positive electrical charge (+1 elementary charge). The number of protons in an atom's nucleus determines an element's identity and is known as the atomic number (Z). For example, every atom with 6 protons is a carbon atom.

Neutrons and Their Role

Neutrons are the other type of particle found in the nucleus. Unlike protons, neutrons have no electrical charge; they are electrically neutral. Neutrons contribute to the mass of the atom and help to stabilise the nucleus, especially in larger atoms, by counteracting the strong repulsive forces between the positively charged protons.

Characteristic Positive Charge of the Nucleus

Because protons are positively charged and neutrons are neutral, the entire atomic nucleus always possesses a net positive electrical charge. The magnitude of this positive charge is directly proportional to the number of protons present. This characteristic positive charge is unique for each element and plays a crucial role in atomic structure and interactions.

Atomic Structure Basics

Every atom consists of a central nucleus surrounded by orbiting electrons. The nucleus contains protons and neutrons. Protons have a positive charge (+1), neutrons have no charge (0), and electrons have a negative charge (-1). The mass of a proton is approximately equal to the mass of a neutron, while electrons have negligible mass in comparison. The number of protons defines the element. In a neutral atom, the number of protons equals the number of electrons.

Understanding Nuclear Notation

The conventional representation for a nucleus is ${A}_{Z}\text{X}$:

• X is the chemical symbol of the element (e.g., C for Carbon, O for Oxygen).
• A is the mass number, which is the total number of protons and neutrons in the nucleus (A = protons + neutrons).
• Z is the atomic number (or proton number), which is the number of protons in the nucleus. This number uniquely identifies the element.

From this notation, you can calculate the number of neutrons by subtracting the atomic number from the mass number: Number of neutrons = A - Z.

What are Isotopes?

Isotopes are atoms of the same element that have different mass numbers. This means they have the same number of protons (same atomic number, Z) but a different number of neutrons. For example, hydrogen has three common isotopes: protium (${1}_{1}\text{H}$, 1 proton, 0 neutrons), deuterium (${2}_{1}\text{H}$, 1 proton, 1 neutron), and tritium (${3}_{1}\text{H}$, 1 proton, 2 neutrons). Because isotopes of an element have the same number of protons and therefore the same electron configuration, they exhibit identical chemical properties.

What is Nuclear Fusion?

Nuclear fusion is a nuclear reaction where two smaller, lighter atomic nuclei combine to form a single, larger, heavier nucleus. This process results in a release of a significant amount of energy. It is the opposite of nuclear fission, where a heavy nucleus splits into lighter nuclei. Fusion powers stars, including the Sun, through reactions involving hydrogen isotopes.

Conditions Required for Fusion

For fusion to occur, extreme conditions are necessary. These include extremely high temperatures and high pressures. The high temperatures provide enough kinetic energy for the positively charged nuclei to overcome their mutual electrostatic repulsion and get close enough to fuse. High pressure helps to contain the plasma, increasing the chances of collisions and fusion. These conditions are found naturally in the core of stars.

Energy Release in Fusion

When two light nuclei fuse, the mass of the resulting single, heavier nucleus is slightly less than the sum of the masses of the original nuclei. This difference in mass is converted into a large amount of energy, as described by Einstein's famous equation, E=mc². This energy release makes fusion a very attractive potential source of power.

Challenges of Controlled Fusion on Earth

Replicating the conditions for nuclear fusion in a controlled manner on Earth is incredibly challenging. Sustaining temperatures in the millions of degrees Celsius, hotter than the Sun's core, and confining the superheated plasma for long enough to generate net energy, are major engineering hurdles. Various confinement methods, such as magnetic confinement and inertial confinement, are being researched.

Balancing Nuclear Equations

Nuclear equations represent radioactive decay and must be balanced. This means the sum of the mass numbers (top numbers) on both sides of the equation must be equal, and the sum of the atomic numbers (bottom numbers, representing charge) on both sides must also be equal. This principle ensures the conservation of mass and charge during radioactive decay. For example, if a nucleus loses two protons and two neutrons, the atomic number decreases by 2 and the mass number decreases by 4.

Alpha Decay

Alpha decay occurs when an unstable nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. An alpha particle can be represented as ⁴₂He or ⁴₂α. When a nucleus undergoes alpha decay, its mass number decreases by 4, and its atomic number decreases by 2. This changes the element to a different one. For example, Uranium-238 (²³⁸₉₂U) decays into Thorium-234 (²³⁴₉₀Th) by emitting an alpha particle: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.

Beta Decay

Beta decay happens when a neutron in an unstable nucleus transforms into a proton, emitting a beta particle (a high-energy electron). A beta particle is represented as ⁰₋₁e or ⁰₋₁β. During beta decay, the mass number of the nucleus remains unchanged because a neutron is replaced by a proton (mass number is conserved). However, the atomic number increases by 1 because a new proton is formed. This also results in a change to a different element. For example, Carbon-14 (¹⁴₆C) decays into Nitrogen-14 (¹⁴₇N) by emitting a beta particle: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e.

Gamma Emission

Gamma emission often accompanies alpha or beta decay, happening when a nucleus has excess energy after another decay process. Gamma rays are high-energy electromagnetic waves, not particles. Therefore, gamma emission does not change the mass number or the atomic number of the nucleus. It simply releases energy, making the nucleus more stable without changing its elemental identity. Gamma rays are represented by the symbol ⁰₀γ. For example, after an alpha decay, the remaining Thorium isotope might be in an excited state, which then emits a gamma ray: ²³⁴₉₀Th* → ²³⁴₉₀Th + ⁰₀γ (where * denotes an excited state).