State the relative charges of protons, neutrons and electrons as +1, 0 and -1 respectively

5.1.2 The nucleus

Learning Objective

State the relative charges of protons, neutrons and electrons as +1, 0 and -1 respectively, and use this information to work with atomic number (Z), mass number (A), nuclide notation, neutrons, and isotopes.

Core Content (Cambridge IGCSE 0625)

Key Concepts

• Atoms consist of a tiny, dense nucleus surrounded by electrons.
• The nucleus contains:
  • Protons – positively charged (+1)
  • Neutrons – electrically neutral (0)
• Electrons orbit the nucleus and carry a negative charge (–1).
• Atomic number (Z) = number of protons = the element’s identity.
• Mass number (A) = total number of protons + neutrons (nucleons).
• Number of neutrons \(N\) = \(A - Z\).
• Nuclide notation \(\,^{A}_{Z}\!X\) identifies a specific nucleus (X = element symbol).
• Isotopes are atoms of the same element (same Z) with different A.

Particle‑Charge Table

Particle	Symbol	Relative charge
Proton	\(p^{+}\)	+1
Neutron	\(n^{0}\)	0
Electron	\(e^{-}\)	–1

Atomic Number, Mass Number and Nuclide Notation

• Atomic number (Z): number of protons in the nucleus.
• Mass number (A): total number of protons + neutrons.
• Nuclide notation: \(\,^{A}_{Z}\!X\) where the subscript is Z and the superscript is A. Example: carbon‑12 is written \(\,^{12}_{6}\!C\).

Calculating Neutrons

The number of neutrons in a nucleus is obtained from:

\[ N = A - Z \]

Worked example

How many neutrons are in \(\,^{23}_{11}\!Na\) (sodium‑23)?

1. Identify \(A = 23\) and \(Z = 11\).
2. Apply the formula: \(N = 23 - 11 = 12\).
3. Therefore, sodium‑23 contains 12 neutrons.

Isotopes

Isotopes are nuclides of the same element (same Z) but with different mass numbers.

Element	Isotope	Notation	Neutrons (N)
Carbon	Carbon‑12	\(\,^{12}_{6}\!C\)	6
Carbon	Carbon‑14	\(\,^{14}_{6}\!C\)	8

Why the Charges Matter

The sum of the charges of all particles in a neutral atom is zero:

\[ \text{Total charge}= Z(+1) + (\text{Number of electrons})(-1) = 0 \]

Neutrons, being neutral, do not affect the charge balance.

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5.1.2 The nucleus – Supplement (Extended Content)

Relationship between proton number and charge

• Each proton contributes a charge of +1 e (where \(e = 1.602\times10^{-19}\,\text{C}\)).
• Therefore the total nuclear charge is \(+Z\,e\).
• Neutrons have no charge, so they do not alter the overall electrical charge of the nucleus.

Mass–energy relationship

When nucleons bind together, a small amount of mass is converted into energy (the binding energy). Qualitatively:

\[ \Delta m \;c^{2} = \text{energy released} \]

Thus, the mass of a nucleus is slightly less than the sum of the masses of its separate protons and neutrons. This principle underlies the large energy output of both fission and fusion.

Nuclear reactions – fission and fusion

Fission (heavy nucleus splits)

\[ ^{235}_{92}\!U + ^{1}_{0}n \;\longrightarrow\; ^{141}_{56}\!Ba + ^{92}_{36}\!Kr + 3\,^{1}_{0}n \]

Check the balance:

• Mass numbers: \(235 + 1 = 236\) on the left; \(141 + 92 + 3\times1 = 236\) on the right.
• Atomic numbers: \(92 + 0 = 92\) on the left; \(56 + 36 + 3\times0 = 92\) on the right.

Fusion (light nuclei combine)

\[ ^{2}_{1}H + ^{3}_{1}H \;\longrightarrow\; ^{4}_{2}He + ^{1}_{0}n \]

Check the balance:

• Mass numbers: \(2 + 3 = 5\); \(4 + 1 = 5\).
• Atomic numbers: \(1 + 1 = 2\); \(2 + 0 = 2\).

Half‑life – definition and worked calculation

Definition: The half‑life (\(t_{1/2}\)) of a radioactive nuclide is the time required for half of the nuclei in a sample to decay.

Worked example

A 80 g sample of a radionuclide has a half‑life of 5 days. How much of the sample remains after 15 days?

1. Determine the number of half‑lives: \(15\text{ days} \div 5\text{ days} = 3\) half‑lives.
2. After each half‑life the mass is halved: \(\displaystyle 80 \rightarrow 40 \rightarrow 20 \rightarrow 10\) g.
3. Therefore, after 15 days, 10 g of the original sample remains.

Safety precautions for ionising radiation

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Check Your Understanding

• What is the relative charge of a proton? Answer: +1.
• What is the relative charge of a neutron? Answer: 0.
• What is the relative charge of an electron? Answer: –1.
• If an atom has 12 protons and 12 electrons, what is its net charge? Answer: 0 (neutral).
• Write the nuclide notation for an atom with 7 protons and 8 neutrons. Answer: \(\,^{15}_{7}\!N\).
• How many neutrons are in \(\,^{40}_{20}\!Ca\)? Answer: 20.