The nuclear atom — OCR A-Level Physics
Test yourself on The nuclear atom with OCR A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
The nuclear atom explained
In the alpha-particle scattering experiment, alpha particles are directed at a very thin gold foil inside an evacuated chamber.
Read the full explanation
A detector, such as a movable microscope and scintillation screen, records where particles arrive. Most alpha particles pass almost straight through, some are deflected through large angles, and a very small number bounce back. This pattern shows that the atom is mostly empty space, with a tiny central nucleus that is positively charged and contains most of the atom's mass. The rare large deflections occur when an alpha particle passes close to a nucleus and experiences a strong electrostatic repulsion.
(b) simple nuclear model of the atom; protons, neutrons and electrons
The simple nuclear model describes an atom as a small, dense, positively charged nucleus surrounded by electrons. The nucleus contains protons, which are positively charged, and neutrons, which are neutral. Together, protons and neutrons are called nucleons. Electrons are negatively charged and occupy the space around the nucleus. In a neutral atom, the number of electrons equals the number of protons, so the total charge is zero. The proton number, or atomic number, gives the number of protons and identifies the element. The nucleon number, or mass number, is the total number of protons and neutrons. Isotopes have the same proton number but different numbers of neutrons.
(c) relative sizes of atom and nucleus
The nucleus is extremely small compared with the whole atom. A typical atomic diameter is of the order of 10⁻¹⁰ m, while a typical nuclear diameter is of the order of 10⁻¹⁵ m to 10⁻¹⁴ m. The ratio of atomic diameter to nuclear diameter is therefore about 10⁵, meaning the atom is roughly one hundred thousand times wider than its nucleus. Because volume depends on the cube of the radius, the atom's volume is about 10¹⁵ times the nuclear volume. This explains why most alpha particles pass straight through the atom in scattering experiments, while only those passing very close to the nucleus are strongly deflected.
(d) proton number; nucleon number; isotopes; notation X Z A for the representation of nuclei
The proton number Z is the number of protons in a nucleus and defines the element. The nucleon number A is the total number of protons and neutrons, so the neutron number is A − Z. Isotopes are nuclei of the same element with the same Z but different A, hence different neutron numbers; they have identical chemical properties but different masses and nuclear stability. Nuclear notation places A as a superscript and Z as a subscript before the symbol X, for example ¹²₆C has Z = 6 and A = 12, so it contains 6 protons and 6 neutrons. For ²³⁵₉₂U, Z = 92 and A = 235, giving 143 neutrons. In an MCQ, identify Z from the subscript and A from the superscript, then calculate neutrons as A − Z. Remember that changing Z changes the element, while changing A alone gives an isotope.
(e) strong nuclear force; short-range nature of the force; attractive to about 3 fm and repulsive below about 0.5 fm
The strong nuclear force acts between nucleons and holds the nucleus together against electrostatic repulsion between protons. It is much stronger than the electrostatic force at nuclear separations but is short-range. Its behaviour depends on the separation between nucleons: at distances greater than about 3 fm it is negligible; between about 0.5 fm and 3 fm it is attractive, with a maximum attraction around 1 fm; below about 0.5 fm it becomes repulsive, preventing nucleons from collapsing into each other. This short-range attraction explains why large nuclei need more neutrons for stability, because the strong force only acts between neighbouring nucleons while electrostatic repulsion acts throughout the nucleus. In an MCQ, compare the separation with the 3 fm and 0.5 fm limits to decide whether the force is attractive, repulsive or negligible.
(f) radius of nuclei; R = r₀A^(1/3) where r₀ is a constant and A is the nucleon number
The radius R of a nucleus is related to its nucleon number A by R = r₀A^(1/3), where r₀ is an empirical constant approximately equal to 1.2 × 10⁻¹⁵ m. This equation shows that nuclear volume is proportional to A, because volume depends on R³ and R³ = r₀³A. The constant r₀ represents the approximate radius of a single nucleon. To use the equation, substitute the nucleon number and evaluate A^(1/3), then multiply by r₀. For example, for A = 64, A^(1/3) = 4, so R = 4r₀ ≈ 4.8 × 10⁻¹⁵ m. In an MCQ, check whether the question asks for radius, volume or density, and remember that A is the total number of nucleons, not just protons.
(g) mean densities of atoms and nuclei.
The mean density of a nucleus is much greater than that of an atom because the mass of an atom is concentrated in a very small nucleus. Atomic radius is typically about 10⁻¹⁰ m, while nuclear radius is about 10⁻¹⁵ m to 10⁻¹⁴ m, so nuclear volume is smaller by a factor of about 10¹⁵. Since almost all atomic mass is in the nucleus, nuclear density is roughly 10¹⁵ times greater than atomic density. Nuclear density is approximately constant for all nuclei because both mass and volume are proportional to nucleon number A. To compare densities, use density = mass/volume, with mass in kg and volume in m³. For a nucleus, mass ≈ A × 1.66 × 10⁻²⁷ kg and volume = (4/3)πR³, giving a density of about 2 × 10¹⁷ kg m⁻³.
Your focus
- Describe the alpha-particle scattering experiment and the pattern of deflections observed.
- Explain how the observations provide evidence for a small, positively charged nucleus.
- Relate large-angle scattering to electrostatic repulsion between alpha particles and nuclei.
Show all 21 objectives
- Describe the simple nuclear model, naming protons, neutrons and electrons and their charges.
- Use proton number and nucleon number to describe the composition of an atom.
- Explain how isotopes differ in neutron number while remaining the same element.
- State the approximate orders of magnitude of atomic and nuclear diameters.
- Calculate the ratio of atomic size to nuclear size and interpret it in terms of empty space.
- Explain how the relative sizes of atom and nucleus relate to alpha-particle scattering observations.
- Define proton number and nucleon number and relate them to the composition of a nucleus.
- Interpret nuclear notation to identify the numbers of protons, neutrons and nucleons.
- Explain what isotopes are and how they differ in nucleon number but not proton number.
- Describe the strong nuclear force and its role in the nucleus.
- State the approximate distance ranges over which the strong force is attractive and repulsive.
- Explain how the short-range nature of the strong force affects nuclear stability.
- Use the equation R = r₀A^(1/3) to calculate nuclear radii.
- Explain the meaning of the constant r₀ and its approximate value.
- Relate the equation to the proportionality between nuclear volume and nucleon number.
- Compare the mean densities of atoms and nuclei.
- Explain why nuclear density is approximately constant for different nuclei.
- Calculate nuclear density using mass and volume.
The nuclear atom exam tips
Marking Points
- Most alpha particles pass straight through the foil, showing that the atom is mostly empty space.
- A small number are deflected through large angles or bounce back, showing that the positive charge and most of the mass are concentrated in a very small nucleus.
- The deflections are caused by electrostatic repulsion between the positive alpha particle and the positive nucleus.
- The experiment used a thin gold foil and a detector to record the scattering pattern at different angles.
- The results rule out a uniform spread of positive charge throughout the atom, because that would not produce large-angle scattering.
- The nucleus contains protons and neutrons, collectively called nucleons.
- Protons are positively charged, neutrons have no charge, and electrons are negatively charged.
- In a neutral atom, the number of electrons equals the number of protons.
- The proton number determines the element, while the nucleon number is the total number of protons and neutrons.
- Isotopes of an element have the same number of protons but different numbers of neutrons.
- A typical atomic diameter is of the order of 10⁻¹⁰ m.
- A typical nuclear diameter is of the order of 10⁻¹⁵ m to 10⁻¹⁴ m.
- The ratio of atomic diameter to nuclear diameter is about 10⁵, so the atom is roughly 100000 times wider than the nucleus.
- Because volume scales with the cube of radius, the atomic volume is about 10¹⁵ times the nuclear volume.
- The large difference in size means the atom is mostly empty space, which is consistent with alpha-particle scattering results.
- Proton number Z is the number of protons in a nucleus and determines the element.
- Nucleon number A is the total number of protons and neutrons in a nucleus.
- The number of neutrons is calculated as A − Z.
- Isotopes are nuclei with the same proton number Z but different nucleon number A, so they have different neutron numbers.
- In the notation X with A as superscript and Z as subscript, the superscript is the nucleon number and the subscript is the proton number.
- For example, ¹²₆C has 6 protons and 6 neutrons; ²³⁵₉₂U has 92 protons and 143 neutrons.
- The strong nuclear force acts between nucleons and is responsible for holding the nucleus together.
- It is a short-range force, becoming negligible beyond about 3 fm.
- It is attractive between nucleons at separations from about 0.5 fm up to about 3 fm.
- It becomes repulsive at separations below about 0.5 fm, preventing nucleon overlap.
- The strong force is much stronger than the electrostatic repulsion between protons at nuclear distances.
- The short-range nature means only neighbouring nucleons interact strongly, which affects nuclear stability.
- The nuclear radius R is given by R = r₀A^(1/3), where A is the nucleon number.
- r₀ is a constant approximately equal to 1.2 × 10⁻¹⁵ m.
- The equation implies that nuclear volume is proportional to A, since volume ∝ R³.
- A is the total number of nucleons (protons plus neutrons), not the proton number.
- To calculate R, evaluate the cube root of A and multiply by r₀.
- For example, for A = 64, R = 4r₀ ≈ 4.8 × 10⁻¹⁵ m.
- The mean density of a nucleus is much greater than the mean density of an atom.
- Atomic radius is about 10⁻¹⁰ m, while nuclear radius is about 10⁻¹⁵ m to 10⁻¹⁴ m.
- Most of the atom's mass is in the nucleus, so nuclear density is roughly 10¹⁵ times atomic density.
- Nuclear density is approximately constant for different nuclei because mass and volume are both proportional to A.
- Density is calculated as mass divided by volume; for a nucleus, mass ≈ A × 1.66 × 10⁻²⁷ kg and volume = (4/3)πR³.
- The nuclear density is of the order of 10¹⁷ kg m⁻³.
Examiner Tips
- 💡Link each observation to a conclusion: straight-through paths show empty space, large deflections show a small charged nucleus.
- 💡Use the word electrostatic repulsion rather than a general force when explaining the deflection.
- 💡Avoid saying the alpha particles hit the nucleus; they are deflected by the electric field near it.
- 💡Use the terms proton number and nucleon number precisely, and state what each counts.
- 💡Check charge balance by comparing the number of protons with the number of electrons in a neutral atom.
- 💡When identifying an isotope, compare proton numbers and neutron numbers rather than total nucleon numbers alone.
- 💡Quote orders of magnitude rather than exact values, and state the unit clearly.
- 💡Show the ratio calculation explicitly, for example 10⁻¹⁰ m divided by 10⁻¹⁵ m equals 10⁵.
- 💡If asked about volume, remember to cube the radius ratio rather than using the diameter ratio directly.
- 💡Read the superscript and subscript carefully; write down Z and A before calculating neutrons as A − Z.
- 💡Check whether the question asks for protons, neutrons or nucleons; each has a different value.
- 💡For isotope questions, confirm that Z is unchanged and only A differs.
- 💡Memorise the approximate distances: attractive up to about 3 fm, repulsive below about 0.5 fm.
- 💡When comparing forces, state that the strong force is much stronger than electrostatic repulsion at nuclear separations.
- 💡Use the short-range nature to explain why neutrons are needed for stability in larger nuclei.
- 💡Write down the equation R = r₀A^(1/3) and substitute values carefully, keeping units consistent.
- 💡Check whether the question gives A or asks you to find it from the notation.
- 💡Remember that r₀ is approximately 1.2 × 10⁻¹⁵ m unless another value is given.
- 💡Use the correct radius: atomic radius ~10⁻¹⁰ m, nuclear radius ~10⁻¹⁵ m.
- 💡Show that nuclear density is roughly constant by noting mass ∝ A and volume ∝ A.
- 💡When calculating density, convert all quantities to SI units before dividing.
Common Mistakes
- Saying alpha particles are attracted to the nucleus: both the alpha particle and the nucleus are positively charged, so the force is repulsive.
- Believing most alpha particles are deflected: most pass through with little or no deflection, and only a very small fraction are strongly deflected.
- Thinking the nucleus is large: the nucleus is extremely small compared with the atom, which is why large-angle scattering is rare.
- Confusing proton number with nucleon number: proton number counts protons only, while nucleon number counts protons plus neutrons.
- Thinking neutrons are charged: neutrons are neutral, so they do not contribute to the electrostatic charge of the nucleus.
- Assuming all atoms of an element have the same mass: isotopes have different numbers of neutrons and therefore different masses.
- Treating the ratio of diameters as the ratio of volumes: volume depends on the cube of the radius, so the volume ratio is about 10¹⁵, not 10⁵.
- Using 10⁻¹⁵ m as the atomic diameter: that is the order of the nuclear diameter, while the atomic diameter is about 10⁻¹⁰ m.
- Thinking the nucleus occupies a large fraction of the atom: the nucleus is tiny, so the atom is mostly empty space.
- Confusing proton number with nucleon number: the subscript is Z (protons) and the superscript is A (nucleons), not the other way round.
- Thinking isotopes have different proton numbers: isotopes of an element all have the same Z but different A.
- Calculating neutron number as A + Z instead of A − Z, which gives an incorrect neutron count.
- Believing that changing the number of neutrons changes the element: the element is fixed by Z, so adding neutrons only creates an isotope.
- Thinking the strong force acts over unlimited distance: it is short-range and negligible beyond about 3 fm.
- Believing the strong force is always attractive: it becomes repulsive below about 0.5 fm.
- Confusing the strong force with the electrostatic force: the strong force acts between all nucleons, while electrostatic repulsion acts only between protons.
- Assuming the strong force acts between protons only: it acts between protons and neutrons and between neutrons themselves.
- Using the proton number Z instead of the nucleon number A in the equation.
- Forgetting to take the cube root of A and instead multiplying r₀ by A.
- Confusing the constant r₀ with the nuclear radius R; r₀ is approximately 1.2 × 10⁻¹⁵ m, while R depends on A.
- Assuming nuclear volume is proportional to A^(1/3) rather than to A; since R ∝ A^(1/3), volume ∝ R³ ∝ A.
- Thinking atomic density is similar to nuclear density: nuclear density is about 10¹⁵ times greater.
- Using the atomic radius instead of the nuclear radius when calculating nuclear density.
- Forgetting that nuclear density is approximately independent of nucleon number, because both mass and volume scale with A.
- Confusing mass number with mass in kg; mass number A is a count, while mass in kg requires multiplying by the nucleon mass.