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)
Core statements (as written in the syllabus)
- State the relative charges of protons, neutrons and electrons as
+1,0and-1respectively. - Define atomic number (Z) and mass number (A); write nuclide notation AZX.
- Calculate the number of neutrons (N) in a nucleus using N = A – Z.
- Identify isotopes as nuclides of the same element (same Z) with different A.
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)?
- Identify \(A = 23\) and \(Z = 11\).
- Apply the formula: \(N = 23 - 11 = 12\).
- 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.
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?
- Determine the number of half‑lives: \(15\text{ days} \div 5\text{ days} = 3\) half‑lives.
- After each half‑life the mass is halved:
\(\displaystyle 80 \rightarrow 40 \rightarrow 20 \rightarrow 10\) g.
- Therefore, after 15 days, 10 g of the original sample remains.
Safety precautions for ionising radiation
- Time: Reduce exposure time as much as possible.
- Distance: Keep as far away from the source as practicable (inverse‑square law).
- Shielding: Use appropriate materials (e.g., lead for gamma rays, acrylic for beta particles, plastic or glass for alpha particles).
- Never look directly at a strong source and always follow laboratory safety rules.
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.
