Explore the constituents of the nucleus, isotopes and specific charge
AQA A-Level Physics 2
🔬State the properties of protons, neutrons and electrons
📝Use nuclide notation ᴬ_Z X correctly
♻️Define isotopes and explain their properties
⚡Calculate specific charge for particles and nuclei
🌐State the approximate size of the nucleus and atom
📏Use R = R₀A^(1/3) for nuclear radius
Constituents of the Atom
Every atom consists of a tiny, dense, positively charged nucleus surrounded by a cloud of negatively charged electrons. The nucleus contains protons and neutrons (collectively called nucleons).
Particle
Charge / C
Mass / kg
Location
Proton
+1.60 × 10⁻¹⁹
1.673 × 10⁻²⁷
Nucleus
Neutron
0
1.675 × 10⁻²⁷
Nucleus
Electron
−1.60 × 10⁻¹⁹
9.11 × 10⁻³¹
Shells (orbits)
The proton has charge +e where e = 1.60 × 10⁻¹⁹ C (the elementary charge). The electron has charge −e. The neutron is electrically neutral.
Proton number (atomic number) Z: The number of protons in the nucleus. This defines which element the atom is.
Nucleon number (mass number) A: The total number of protons plus neutrons in the nucleus.
Neutron number N: N = A − Z
In a neutral atom, the number of electrons equals the number of protons (Z). An ion has gained or lost electrons, giving it a net charge.
Nuclide Notation
A nuclide is a specific combination of proton number and neutron number. We write it using the standard notation:
ᴬ_Z X
Where: A = mass number (top), Z = proton number (bottom), X = chemical symbol
Example: ²³₁₁Na means sodium with mass number 23 and proton number 11. Neutron number = 23 − 11 = 12.
Other examples you will encounter:
Nuclide
Z (protons)
A (nucleons)
N (neutrons)
¹H (hydrogen)
1
1
0
⁴He (helium)
2
4
2
¹²C (carbon-12)
6
12
6
²³⁵U (uranium)
92
235
143
Isotopes
Isotopes are atoms of the same element (same proton number Z) that have different numbers of neutrons (different mass number A). They have identical chemical properties but different physical properties (mass, nuclear stability).
Examples of isotopes of hydrogen:
Name
Symbol
Protons
Neutrons
Protium (ordinary H)
¹H
1
0
Deuterium
²H
1
1
Tritium
³H
1
2
Isotopes of carbon: ¹²C (stable), ¹³C (stable), ¹⁴C (radioactive — used in carbon dating).
Isotopes have the same chemical symbol and the same number of electrons in a neutral atom. Their chemical behaviour is essentially identical. Their nuclear behaviour (stability, decay mode) can differ greatly.
Specific Charge & Nuclear Radius
Specific charge is the charge-to-mass ratio of a particle. It is measured in C kg⁻¹.
Specific charge = Q / m (C kg⁻¹)
For a proton: specific charge = 1.60 × 10⁻¹⁹ / 1.673 × 10⁻²⁷ = 9.58 × 10⁷ C kg⁻¹
For an electron: specific charge = 1.60 × 10⁻¹⁹ / 9.11 × 10⁻³¹ = 1.76 × 10¹¹ C kg⁻¹
The electron has a much higher specific charge than the proton because it is approximately 1836 times lighter. The specific charge of a nucleus = Ze / (A × mp) approximately.
Nuclear radius: Nuclei are approximately spherical. Their radius follows:
R = R₀ × A^(1/3)
where R₀ ≈ 1.2 × 10⁻¹⁵ m (1.2 fm)
The atom has a radius of approximately 10⁻¹⁰ m (0.1 nm), while the nucleus has a radius of approximately 10⁻¹⁵ m (1 fm) — roughly 10,000 to 100,000 times smaller than the atom. This means the atom is mostly empty space.
Write the nuclide notation for an atom with 17 protons and 20 neutrons. Identify the element.
1Z = protons = 17 → element is Chlorine (Cl)
2A = protons + neutrons = 17 + 20 = 37
³⁷₁₇Cl — Chlorine-37
Calculate the specific charge of a nucleus of ⁴He (alpha particle). Charge = 2e, mass ≈ 4 × mp.
Calculate the radius of a uranium-235 nucleus (A = 235), given R₀ = 1.2 × 10⁻¹⁵ m.
1R = R₀ × A^(1/3)
2A^(1/3) = 235^(1/3) = 6.17
3R = 1.2 × 10⁻¹⁵ × 6.17 = 7.40 × 10⁻¹⁵ m
R = 7.4 × 10⁻¹⁵ m ≈ 7.4 fm
State two similarities and two differences between ¹²C and ¹⁴C.
1Both have Z = 6 (6 protons) → same element, same chemical symbol
2Similarities: same number of protons (6); same number of electrons in neutral atom (6); same chemical properties
3Differences: ¹²C has 6 neutrons; ¹⁴C has 8 neutrons. ¹⁴C is radioactive (beta emitter); ¹²C is stable. Different mass numbers (12 vs 14).
Isotopes — same Z, different A (different neutron numbers)
1. An atom has nuclide notation ⁵⁶₂₆Fe. How many neutrons does it have?
N = A − Z = 56 − 26 = 30 neutrons.
2. Which of the following pairs are isotopes of the same element?
Isotopes have the same Z (same element). ¹⁶O and ¹⁸O both have Z=8 (oxygen) but different A. The others have different elements.
3. Which particle has the highest specific charge?
The electron has specific charge ≈ 1.76 × 10¹¹ C kg⁻¹, much larger than the proton (9.58 × 10⁷ C kg⁻¹) because the electron is ~1836 times lighter. Neutrons have zero charge so their specific charge is zero.
4. What is the approximate ratio of the radius of an atom to the radius of its nucleus?
Atom radius ≈ 10⁻¹⁰ m; nucleus radius ≈ 10⁻¹⁵ m. Ratio = 10⁻¹⁰ / 10⁻¹⁵ = 10⁵ = 100 000. The atom is mostly empty space.
5. Calculate the specific charge (in C kg⁻¹) of a proton. Give your answer to 3 s.f.
1. The radius of a ¹²C nucleus is measured as 2.75 × 10⁻¹⁵ m. Use R = R₀A^(1/3) to find R₀, and compare with the accepted value of 1.2 × 10⁻¹⁵ m. Calculate the % difference.
R₀ = R / A^(1/3) = 2.75 × 10⁻¹⁵ / 12^(1/3) = 2.75 × 10⁻¹⁵ / 2.289 = 1.201 × 10⁻¹⁵ m. % difference = (1.201 − 1.2)/1.2 × 100 = 0.08% — excellent agreement with the accepted value.
2. An ion ⁶³₂₉Cu²⁺ has lost 2 electrons. Calculate its specific charge. (mp = 1.673 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C; assume mass of electrons is negligible.)
Charge = 2e = 2 × 1.60 × 10⁻¹⁹ = 3.20 × 10⁻¹⁹ C. Mass ≈ 63 × m_p = 63 × 1.673 × 10⁻²⁷ = 1.054 × 10⁻²⁵ kg. Specific charge = 3.20 × 10⁻¹⁹ / 1.054 × 10⁻²⁵ = 3.04 × 10⁶ C kg⁻¹.
3. Explain why isotopes of the same element have identical chemical properties but different physical properties. Give one example of a physical property that differs between isotopes.
Chemical properties depend on the number and arrangement of electrons in the atom, which equals the number of protons (Z). Since isotopes have the same Z, they have the same electron configuration → identical chemistry. Physical properties such as mass, density, nuclear stability, rate of radioactive decay, and melting/boiling points (for pure samples) depend on the number of neutrons — which differs between isotopes. Example: ¹⁴C is radioactive with a half-life of 5730 years; ¹²C is stable.