use the unified atomic mass unit (u) as a unit of mass

Atoms, Nuclei and Radiation – Unified Atomic Mass Unit (u)

What is the unified atomic mass unit?

The unified atomic mass unit, written as u, is a convenient way to talk about the mass of sub‑atomic particles and atoms. It is defined as one‑twelth of the mass of a carbon‑12 atom:

$$m_u = \frac{1}{12} m_{\text{C-12}}$$

In kilograms this is:

$$m_u = 1.66053906660 \times 10^{-27}\,\text{kg}$$

Think of it as a “mini‑unit” that lets us compare the masses of protons, neutrons, electrons and whole atoms without dealing with huge or tiny numbers.

Masses of common particles (in u)

Using u in calculations

1. Write the mass of the nucleus as Z × m_p + N × m_n, where Z is the number of protons and N the number of neutrons.
2. Subtract the actual atomic mass (including electrons) to find the mass defect:

$$\Delta m = (Z\,m_p + N\,m_n) - m_{\text{atom}}$$

3. Convert the mass defect to energy using Einstein’s equation E = Δm c² (remember to convert u to kg first).

⚛️ Analogy: Imagine the nucleus as a pile of Lego bricks (protons and neutrons). When you glue them together, a tiny bit of mass disappears – that’s the mass defect, and it’s released as energy.

Example: Mass defect of Carbon‑12

Carbon‑12 has 6 protons and 6 neutrons. Its atomic mass is 12.000000 u.

Calculate Δm:

$$\Delta m = (6\times1.007276 + 6\times1.008665) - 12.000000 = 0.072 \text{ u}$$

Convert to kg: Δm = 0.072 × 1.66054×10⁻²⁷ kg = 1.1956×10⁻²⁶ kg.

Energy released: E = Δm c² = 1.1956×10⁻²⁶ kg × (3.00×10⁸ m/s)² ≈ 1.07×10⁻⁹ J.

Types of radiation

• ⚡ Alpha (α) – 2 protons + 2 neutrons (helium nucleus). Heavy, low penetration.
• 🌀 Beta (β) – high‑speed electron or positron. Medium penetration.
• 💡 Gamma (γ) – high‑energy photons. Very high penetration.

Nuclear reactions

Two main processes:

1. Fusion – light nuclei combine to form a heavier nucleus, releasing energy. Example: ⁴He + ⁴He → ⁸Be.
2. Fission – a heavy nucleus splits into lighter nuclei, also releasing energy. Example: ²³⁵U + n → ²³⁸Ba + ³⁹Kr + 3n.

Both processes involve a mass defect and thus energy release.

Key takeaway

The unified atomic mass unit (u) is a handy “unit‑box” that lets us talk about atomic masses in a tidy, comparable way. By using u, we can easily calculate mass defects, binding energies and understand the energy behind nuclear reactions.

💡 Remember: 1 u ≈ 1.66×10⁻²⁷ kg. Keep this conversion handy for all your physics calculations!