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Atomic Mass

Key idea: Define the unified atomic mass unit u, convert between u and kg, and use atomic masses in nuclear calculations (A Level Physics).

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Interpret nuclear structure, isotopes and Rutherford scattering.

1. Definitions (Must Know)

A. Unified atomic mass unit, u

One unified atomic mass unit, u, is defined as:

one-twelfth of the mass of a neutral carbon-12 atom.

Numerically: 1 u ≈ 1.66 × 10⁻²⁷ kg

B. Avogadro constant, N_A

The Avogadro constant is: N_A ≈ 6.02 × 10²³ mol⁻¹

C. Relative atomic mass, mᵣ

The relative atomic mass, mᵣ, is the ratio: mᵣ = (mass of an atom)/(1 u)

It is dimensionless.

Why this matters in nuclear physics

Atomic masses are often tabulated in u. Converting between u and kg lets you use E = mc² to find binding energies and energy released in nuclear reactions.

2. Key Ideas (What Earns Marks)

  • Definition to quote: 1 u is 1/12 of the mass of a carbon-12 atom.
  • Conversions you use constantly:
    • m(kg) = m(u) (1.66 × 10⁻²⁷)
    • m(u) = m(kg)/(1.66 × 10⁻²⁷)
  • mᵣ is dimensionless (it is a ratio).

3. Detailed Explanations

A. Getting the value of 1u

Since 1 mole of carbon-12 has mass 0.012 kg and contains N_A atoms, the mass of one carbon-12 atom is: m(C-12) = 0.012/N_A

So: 1u = 1/12 m(C-12) = 0.012/12N_A ≈ 1.66 × 10⁻²⁷ kg

4. Common Mistakes

  • Treating u as a unit of “nucleon number” (it’s a mass unit, not A).
  • Forgetting that mᵣ has no units.
  • Using 6.02 × 10²³ without units (it is mol⁻¹).

5. Exam Tips

  • If a question gives masses in u, stay in u as long as possible and convert at the end.
  • In energy-release questions, you may use:
    • 1 u c² ≈ 931 MeV (if given/allowed), or convert to joules using E = mc².

6. Worked Examples

Modelled example 1

Convert u to kg

Core

Problem

Find the mass in kilograms of an atom whose mass is 4.00 u.
Study the worked solution

  1. Use the mass-unit conversion

    Method

    Multiply by 1.66 × 10⁻²⁷ kg/u.

    Reason

    Each atomic mass unit contributes this many kilograms.

    Working

    m = (4.00 u)(1.66 × 10⁻²⁷ kg/u)

  2. Evaluate

    Method

    m = 6.64 × 10⁻²⁷ kg.

    Reason

    The u units cancel, leaving kilograms.

    Working

    m = 6.64 × 10⁻²⁷ kg

Common misconception 2

Convert kg to u

Find and correct the mistake

Learner claim

A particle has mass 3.32 × 10⁻²⁷ kg. A learner multiplies by 1.66 × 10⁻²⁷ to convert it to u. Diagnose the conversion direction and find the mass in u.

Try this before viewing the solution

Unit: u

View solution step by step

  1. Choose the inverse conversion

    Method

    Divide the mass in kilograms by 1.66 × 10⁻²⁷ kg/u.

    Reason

    The question asks how many atomic mass units fit into the given mass.

    Working

    m(u) = (3.32 × 10⁻²⁷ kg)/(1.66 × 10⁻²⁷ kg/u)

  2. Evaluate

    Method

    m = 2.00 u.

    Reason

    Kilograms cancel and the quotient retains u.

    Working

    m = 2.00 u

7. Mind Stretchers

Mind stretcher 1: Quick estimate checkExtension

Why is it reasonable that a proton has mass about 1u?

Show Answer

Nucleon masses are about 1.67 × 10⁻²⁷ kg, and 1u ≈ 1.66 × 10⁻²⁷ kg, so they are very close. That’s why nuclear/atomic masses are naturally tabulated in u.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027