The nucleus Revision Notes

The nucleus is the small, dense centre of an atom where almost all of its mass is concentrated. It is extremely small compared to the overall size of the atom, typically about 1 femtometre (1 fm = 1 × 10⁻¹⁵ m) in radius.

The nucleus contains two types of subatomic particles: protons and neutrons. These particles are collectively known as nucleons.

• Nucleus radius ~ 1 fm (1 × 10⁻¹⁵ m)
• Contains protons and neutrons (nucleons)
• Almost all atomic mass is in the nucleus

Protons are positively charged particles found in the nucleus. Each proton carries a charge of +1 elementary charge (+1e), where e = 1.6 × 10⁻¹⁹ coulombs.

The number of protons in the nucleus defines the atomic number (Z) of an element, which determines the chemical identity of the atom.

Protons have a relative mass of approximately 1 atomic mass unit (u), which is about 1.67 × 10⁻²⁷ kg.

• Charge: +1e (1.6 × 10⁻¹⁹ C)
• Relative mass: ~1 u (1.67 × 10⁻²⁷ kg)
• Determines atomic number and element identity

Neutrons are neutral particles found in the nucleus alongside protons. They carry no electric charge (charge = 0).

Neutrons have a mass very close to that of protons, about 1 u (1.67 × 10⁻²⁷ kg).

Neutrons contribute to the mass of the nucleus and play a key role in stabilising it by reducing the electrostatic repulsion between protons.

• Charge: 0 (neutral)
• Relative mass: ~1 u (1.67 × 10⁻²⁷ kg)
• Contribute to nuclear stability

Protons and neutrons together are called nucleons. The total number of nucleons in a nucleus is called the nucleon number or mass number (A).

Despite protons repelling each other due to their positive charges, the nucleus remains stable because nucleons are held together by the strong nuclear force.

The strong nuclear force is a powerful, short-range force that acts between nucleons, overcoming the electrostatic repulsion between protons and binding the nucleus together.

• Nucleons = protons + neutrons
• Mass number (A) = total nucleons
• Strong nuclear force binds nucleons

The nucleus is the dense central part of an atom made up of protons and neutrons.

Protons are positively charged and determine the element's identity.

Neutrons are neutral and help stabilise the nucleus by reducing repulsion between protons and adding mass to the nucleus.

• Nucleus contains protons (+ charge) and neutrons (neutral)
• Nucleons held together by strong nuclear force
• Atomic number = number of protons; mass number = total nucleons

Atoms are composed of smaller particles called subatomic particles. The three main types are protons, neutrons, and electrons. Each has distinct properties including mass and electric charge, which determine the atom's overall behaviour and interactions with other atoms.

Understanding the relative charges of these particles is fundamental to grasping atomic structure and the forces within an atom.

• Protons, neutrons, and electrons are the primary constituents of atoms.
• Each particle has a characteristic electric charge.
• The arrangement and charge of these particles influence chemical and physical properties.

The electric charge of a particle is a fundamental property that causes it to experience a force in an electric field. Charges are measured relative to the elementary charge, denoted as +1 or -1 in relative terms.

Protons carry a positive charge, assigned a relative charge of +1.

Neutrons carry no electric charge, so their relative charge is 0 (neutral). They do not contribute to the atom's overall charge but add to its mass and stability of the nucleus. Electrons carry a negative charge, with a relative charge of -1, equal in magnitude but opposite in sign to that of protons.

• Proton charge: +1 (positive)
• Neutron charge: 0 (neutral)
• Electron charge: -1 (negative)

The positive charge of protons in the nucleus attracts the negatively charged electrons, which orbit the nucleus. This electrostatic attraction holds the atom together.

Since neutrons have no charge, they do not affect the electrostatic forces but contribute to the mass and stability of the nucleus by reducing repulsive forces between protons.

The balance between the number of protons and electrons determines the overall charge of the atom. If equal, the atom is electrically neutral; if not, it becomes an ion with positive or negative charge.

• Electrostatic attraction between protons and electrons binds the atom.
• Neutrons stabilise the nucleus without affecting charge.
• Charge balance determines whether an atom is neutral or an ion.

Electric charge is measured in coulombs (C). The elementary charge (charge of a single proton or electron) is approximately 1.6 × 10⁻¹⁹ C.

In relative terms, the proton's charge is +1, the electron's charge is -1, and the neutron's charge is 0. This relative scale is used for simplicity in atomic physics.

The actual charge of a proton is +1.6 × 10⁻¹⁹ C, and the electron's charge is -1.6 × 10⁻¹⁹ C, exactly equal in magnitude but opposite in sign.

• Charge unit: coulomb (C)
• Elementary charge magnitude: 1.6 × 10⁻¹⁹ C
• Relative charges simplify atomic calculations

When drawing atomic diagrams, represent protons with a '+' sign to indicate positive charge, neutrons with '0' or no sign to indicate neutrality, and electrons with a '−' sign to indicate negative charge.

A simple nucleus diagram shows protons and neutrons clustered together, with electrons shown orbiting the nucleus.

This visual helps understand how charges are distributed within an atom and how they influence atomic behaviour.

• Protons: labelled with '+'
• Neutrons: labelled with '0' or no charge
• Electrons: labelled with '−'
• Electrostatic attraction shown by arrows between protons and electrons

The proton number, also known as the atomic number and symbolised by Z, is the number of protons present in the nucleus of an atom.

Each element is uniquely identified by its proton number; for example, all atoms with Z = 6 are carbon atoms.

Since protons carry a positive charge of +1 elementary charge, the proton number also determines the positive charge of the nucleus and the element's chemical properties.

• Proton number (Z) = number of protons in the nucleus
• Defines the element identity
• Protons have charge +1

The nucleon number, symbolised by A, is the total number of nucleons in the nucleus, where nucleons are protons and neutrons.

It represents the total mass of the nucleus in terms of the count of these particles, as protons and neutrons have approximately equal mass.

The nucleon number is always a whole number and is used to distinguish isotopes of the same element, which have the same Z but different A.

• Nucleon number (A) = number of protons + number of neutrons
• Represents the total nucleons in the nucleus
• Used to identify isotopes

Since the nucleon number is the sum of protons and neutrons, the number of neutrons in a nucleus can be found by subtracting the proton number from the nucleon number.

This relationship is expressed by the formula: Number of neutrons = A - Z.

Knowing the number of neutrons is important for understanding nuclear stability and isotopes.

• Number of neutrons = nucleon number (A) - proton number (Z)
• Neutrons have no charge (0)
• Neutrons contribute to nuclear mass and stability

Consider an atom of carbon-14, which has a nucleon number A = 14 and proton number Z = 6.

Using the formula: Number of neutrons = A - Z = 14 - 6 = 8.

Therefore, carbon-14 has 8 neutrons in its nucleus.

• Example: Carbon-14 (A=14, Z=6)
• Neutrons = 14 - 6 = 8
• Units: proton and neutron counts are dimensionless

To draw a simple diagram of a nucleus: start with a circle representing the nucleus.

Inside, draw small circles labelled 'p' to represent protons and 'n' to represent neutrons.

Ensure the total number of protons equals Z and the total number of nucleons (protons + neutrons) equals A.

• Draw a circle for the nucleus
• Inside, draw Z protons labelled 'p'
• Draw (A - Z) neutrons labelled 'n'
• Example: For carbon-14, draw 6 protons and 8 neutrons

Nuclide notation is a concise way to represent the identity and composition of an atomic nucleus. It provides information about the element, the number of protons, and the total number of nucleons (protons plus neutrons) in the nucleus.

The general form of nuclide notation is \(^{A}_{Z}X\), where:

\(X\) is the chemical symbol of the element (e.g., C for carbon, O for oxygen). \(Z\) is the atomic number, the number of protons in the nucleus. It is written as a subscript to the left of the element symbol. \(A\) is the mass number (also called nucleon number), the total number of protons and neutrons in the nucleus. It is written as a superscript to the left of the element symbol.

• Example: Carbon-12 is written as \(^{12}_{6}C\), where 6 is the atomic number and 12 is the mass number.
• The atomic number \(Z\) defines the element and its chemical properties.
• The mass number \(A\) defines the isotope of the element.

1. Atomic Number (\(Z\)) – This is the number of protons in the nucleus. It determines the element's identity and its position in the periodic table. For example, \(Z=6\) corresponds to carbon.

2. Mass Number (\(A\)) – This is the total number of nucleons (protons + neutrons) in the nucleus. It is always a whole number and is approximately equal to the atomic mass in atomic mass units (u).

3. Chemical Symbol (\(X\)) – This is the one- or two-letter symbol representing the element, derived from its English or Latin name.

• Number of neutrons = \(A - Z\).
• Isotopes of an element have the same \(Z\) but different \(A\).

Given a nuclide notation \(^{A}_{Z}X\), you can determine:

Number of protons = \(Z\) (atomic number). Number of neutrons = \(A - Z\). Number of nucleons = \(A\) (mass number).

• Example: For \(^{14}_{6}C\), number of protons = 6, neutrons = 14 - 6 = 8, nucleons = 14.

Isotopes are atoms of the same element (same \(Z\)) but with different numbers of neutrons (different \(A\)). Nuclide notation clearly shows this difference.

For example: \(^{12}_{6}C\) and \(^{14}_{6}C\) are isotopes of carbon. Both have 6 protons but differ in neutron number (6 and 8 respectively).

This notation directly affects the result in nuclear physics to identify specific isotopes involved in reactions or decay processes.

• Isotopes have identical chemical properties but different nuclear properties.
• Nuclide notation helps track nuclear reactions by showing changes in \(A\) and \(Z\).

To draw nuclide notation: 1. Write the chemical symbol \(X\) of the element in the centre.

2. Write the mass number \(A\) as a superscript to the top left of \(X\).

3. Write the atomic number \(Z\) as a subscript to the bottom left of \(X\).

• Example: For oxygen-16, write \(^{16}_{8}O\).
• This clear layout helps in visualising nuclear composition quickly.

Isotopes are atoms of the same chemical element that have the same number of protons (atomic number) but different numbers of neutrons in their nuclei. Because the number of protons defines the element, isotopes belong to the same element but differ in mass number (nucleon number).

The atomic number (Z) is the number of protons in the nucleus, which determines the chemical properties of the element. The mass number (A) is the total number of protons and neutrons in the nucleus. Isotopes have the same Z but different A values.

• Isotopes have identical atomic numbers (Z).
• Isotopes differ in neutron number, resulting in different mass numbers (A).

A common example is carbon, which has several isotopes. Carbon-12 (¹²C) has 6 protons and 6 neutrons, while carbon-14 (¹⁴C) has 6 protons and 8 neutrons. Both are carbon atoms because they have 6 protons, but their mass numbers differ due to the neutron count.

Notation for isotopes is written as \(^{A}_{Z}X\), where X is the chemical symbol, A is the mass number, and Z is the atomic number. For example, carbon-14 is written as \(^{14}_{6}C\).

• Carbon-12: 6 protons, 6 neutrons (mass number 12).
• Carbon-14: 6 protons, 8 neutrons (mass number 14).
• Nuclide notation: \(^{A}_{Z}X\).

Isotopes can be stable or unstable (radioactive). Stable isotopes do not change over time, while radioactive isotopes decay by emitting radiation to reach a more stable state.

The difference in neutron number affects the nuclear stability but not the chemical properties, which depend mainly on the number of protons and electrons.

Radioactive isotopes have practical uses in medicine (e.g., medical imaging, cancer treatment) and archaeology (e.g., carbon dating).

• Stable isotopes remain unchanged over time.
• Radioactive isotopes emit radiation and decay.
• Chemical properties depend on proton number, not neutron number.

Isotopes are used in various scientific and practical fields. For example, carbon-14 dating helps determine the age of archaeological samples by measuring radioactive decay.

In medicine, radioactive isotopes are used as tracers in diagnostic imaging or to treat diseases such as cancer.

Understanding isotopes is essential in nuclear physics, chemistry, and environmental science.

• Carbon-14 dating in archaeology.
• Radioactive tracers in medical imaging.
• Cancer treatment using radioactive isotopes.

Nuclear fission is a process in which a heavy, unstable nucleus splits into two or more smaller nuclei, called fission products. This splitting releases a significant amount of energy and additional neutrons.

Fission usually occurs when a heavy nucleus, such as uranium-235 or plutonium-239, absorbs a slow-moving neutron. The nucleus becomes unstable and splits into smaller nuclei, releasing energy and neutrons.

The released neutrons can then induce fission in other nearby nuclei, creating a chain reaction if conditions allow. This principle is used in nuclear reactors and atomic bombs.

• Heavy nucleus absorbs a neutron → becomes unstable → splits into smaller nuclei.
• Energy is released due to the mass difference before and after fission.
• Additional neutrons are emitted, which can cause further fission reactions.
• Example nuclide equation for uranium-235 fission:
• \[ \mathrm{^{235}_{92}U} + \mathrm{^{1}_{0}n} \rightarrow \mathrm{^{141}_{56}Ba} + \mathrm{^{92}_{36}Kr} + 3\mathrm{^{1}_{0}n} \]
• Here, uranium-235 absorbs a neutron and splits into barium-141, krypton-92, and three neutrons.

Nuclear fusion is the process where two light nuclei combine to form a heavier nucleus. This process releases energy because the mass of the resulting nucleus is less than the sum of the original masses.

Fusion requires extremely high temperatures and pressures to overcome the electrostatic repulsion between positively charged nuclei. Such conditions exist naturally in the cores of stars, including the Sun.

Fusion reactions power stars and have potential for future energy generation on Earth, though controlling fusion is technologically challenging.

• Two light nuclei combine to form a heavier nucleus.
• Energy is released due to the mass difference before and after fusion.
• High temperature and pressure are necessary to overcome repulsion between nuclei.
• Example nuclide equation for fusion of deuterium and tritium:
• \[ \mathrm{^{2}_{1}H} + \mathrm{^{3}_{1}H} \rightarrow \mathrm{^{4}_{2}He} + \mathrm{^{1}_{0}n} \]
• Deuterium and tritium nuclei fuse to form helium-4 and a neutron.

Both fission and fusion involve changes in mass that correspond to changes in energy, according to Einstein's mass-energy equivalence principle, expressed as:

\[ E = mc^2 \] where \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light in vacuum (approximately \(3.0 \times 10^8 \, \mathrm{m/s}\)).

In fission, the total mass of the fission products and emitted neutrons is less than the original mass of the heavy nucleus and the absorbed neutron. The 'missing' mass has been converted into energy, released mainly as kinetic energy of the products and radiation (gamma rays). Similarly, in fusion, the mass of the fused nucleus is less than the sum of the original nuclei, and the mass difference is released as energy.

• Mass before reaction > mass after reaction; mass difference \(\Delta m\) converts to energy.
• Energy released can be calculated by \(E = \Delta m \times c^2\) (qualitative understanding only).
• Energy appears as kinetic energy of particles and electromagnetic radiation.
• This energy release is the source of power in nuclear reactors (fission) and stars (fusion).

Nuclide notation \(^{A}_{Z}X\) is used to represent nuclei, where \(A\) is the nucleon number (total protons and neutrons), \(Z\) is the proton number (atomic number), and \(X\) is the chemical symbol.

In nuclear reactions, the sum of proton numbers and nucleon numbers must be conserved.

For example, in the uranium-235 fission reaction: \[ \mathrm{^{235}_{92}U} + \mathrm{^{1}_{0}n} \rightarrow \mathrm{^{141}_{56}Ba} + \mathrm{^{92}_{36}Kr} + 3\mathrm{^{1}_{0}n} \] the total nucleon number before and after is 236, and the total proton number is 92, showing conservation of nucleons and charge.

• Use nuclide notation to write nuclear reactions.
• Check conservation of nucleon number and proton number in equations.
• Fission example: uranium-235 absorbs neutron and splits into smaller nuclei plus neutrons.
• Fusion example: two light nuclei combine to form a heavier nucleus plus other particles.

Fission reactions occur in nuclear reactors where controlled chain reactions produce heat for electricity generation. Uncontrolled fission reactions cause nuclear explosions.

Fusion reactions power stars, where extreme temperature and pressure allow nuclei to overcome repulsion and fuse.

On Earth, fusion requires devices like tokamaks or inertial confinement to achieve necessary conditions, with the goal of clean energy production.

• Fission: occurs in heavy nuclei, initiated by neutron absorption, used in nuclear power and weapons.
• Fusion: occurs in light nuclei under extreme conditions, powers stars, potential future energy source.
• Both processes release large amounts of energy from small mass changes.

The proton number, also called the atomic number and symbolised by Z, is the number of protons present in the nucleus of an atom.

Protons are positively charged particles found in the nucleus, each with a charge of +1 (in relative units).

The proton number uniquely identifies an element; for example, all atoms with Z = 6 are carbon atoms.

• Proton number (Z) = number of protons in the nucleus
• Each proton has a relative charge of +1
• Z determines the element's identity

The nucleus contains protons and neutrons. Neutrons have no charge (0), so they do not affect the nucleus charge.

Since each proton has a charge of +1, the total charge of the nucleus is equal to the proton number.

Therefore, the nucleus has a positive charge equal to +Z in relative units.

• Neutron charge = 0 (neutral)
• Nucleus charge = number of protons × +1
• Nucleus charge = +Z

The positive charge of the nucleus attracts the negatively charged electrons, holding them in orbit around the nucleus.

The proton number determines the chemical properties of the atom because it defines the number of electrons in a neutral atom.

Changes in proton number change the element, while changes in neutron number create isotopes of the same element.

• Positive nucleus attracts electrons
• Proton number = number of electrons in neutral atom
• Proton number defines element identity

To draw a nucleus: draw a small circle representing the nucleus.

Inside, draw a number of small circles labelled 'p' for protons and 'n' for neutrons.

Label the number of protons as Z and note each proton has charge +1, so total charge = +Z.

• Draw nucleus as a circle
• Inside, draw protons (p) and neutrons (n)
• Label proton number Z and charge +Z

The proton number (Z) equals the number of protons in the nucleus.

Each proton carries a positive charge of +1 (relative charge).

The total charge of the nucleus is therefore +Z, making the nucleus positively charged.

• Proton number = number of protons
• Each proton charge = +1
• Nucleus charge = +Z

The nucleon number, often denoted by A, is the total count of protons and neutrons in the nucleus of an atom. Protons and neutrons are collectively called nucleons.

The relative mass of a nucleus is a dimensionless quantity that compares the mass of that nucleus to one twelfth of the mass of a carbon-12 atom. This relative mass is approximately equal to the nucleon number because each nucleon has a mass close to 1 atomic mass unit (1 amu).

• Nucleon number (A) = number of protons + number of neutrons
• Relative mass of nucleus ≈ nucleon number (A)
• 1 atomic mass unit (amu) ≈ mass of one nucleon

Each proton and neutron has a mass close to 1 atomic mass unit (amu), approximately 1.67 × 10⁻²⁷ kg. Because the nucleus is composed almost entirely of these nucleons, the total mass of the nucleus is roughly the sum of the masses of all its protons and neutrons.

The small differences in mass arise due to the nuclear binding energy, which causes the actual mass of the nucleus to be slightly less than the sum of the individual nucleon masses (mass defect). However, for the purpose of relative mass, this difference is negligible.

Therefore, the nucleon number provides a good estimate of the relative mass of the nucleus.

• Mass of proton ≈ 1 amu
• Mass of neutron ≈ 1 amu
• Mass defect causes nucleus mass to be slightly less than sum of nucleons

Since each nucleon contributes approximately 1 amu, the relative mass of a nucleus can be found by counting the total number of nucleons it contains.

For example, a nucleus with 6 protons and 6 neutrons has a nucleon number A = 12, so its relative mass is about 12 amu.

This relationship allows quick comparison of nuclear masses without complex calculations.

• Relative mass ≈ nucleon number (A)
• Example: Carbon-12 nucleus has A = 12, relative mass ≈ 12 amu

To illustrate, draw a simple labelled diagram of a nucleus showing protons and neutrons as small circles clustered together.

Label the total number of protons (Z) and neutrons (N), and indicate that nucleon number A = Z + N.

This visual helps reinforce that the sum of nucleons determines the nucleus's relative mass.

• Draw clustered protons and neutrons inside nucleus
• Label proton number (Z) and neutron number (N)
• Show nucleon number A = Z + N

Understanding the relationship between nucleon number and relative mass is fundamental in nuclear physics, including isotope identification and nuclear reactions.

It helps in calculating atomic masses, understanding isotopic variations, and interpreting nuclear equations.

This concept is foundational for further study of nuclear stability, binding energy, and radioactive decay.

• Nucleon number essential for isotope identification
• Relative mass aids in atomic mass calculations
• Foundation for nuclear reaction analysis