OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
The nuclear atom: (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.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 7 of 7
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
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.
What earns the marks
- 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.
Common mistakes and how to put them right
Thinking atomic density is similar to nuclear density.
Put it right: 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.
Put it right: Mass number A is a count, while mass in kg requires multiplying by the nucleon mass.
Exam tips
- 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.
Try the lesson
The start of the The nuclear atom: (g) mean densities of atoms and nuclei. lesson, made from checked teaching notes for this specification point.
Listen
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. A strong answer earns marks for these points. 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. Exam tip: Use the correct radius: atomic radius ~10⁻¹⁰ m, nuclear radius ~10⁻¹⁵ m.
Key words
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Atomic and nuclear density
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Mass-volume relationship
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Scale of the atom
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See every definition
- Atomic and nuclear density
- 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.
- Mass-volume relationship
- Density is calculated as mass divided by volume, with mass in kg and volume in m³.
- Scale of the atom
- 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.
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