represent α- and β-decay by a radioactive decay equation of the form UT h92238 90234

What’s a nucleus?

Think of an atom as a tiny solar system. The nucleus is the dense, positively charged “sun” at the centre, made of protons and neutrons. The electrons orbit around it like planets.

• Protons: +1 charge, mass ≈ 1 u
• Neutrons: 0 charge, mass ≈ 1 u
• Electrons: –1 charge, mass ≈ 0 u (negligible for nuclear mass)

Why do nuclei change?

Some nuclei are like unbalanced batteries. They release energy by rearranging themselves into a more stable configuration. This process is called radioactive decay.

1. α‑decay: emits a helium nucleus (2 protons + 2 neutrons)
2. β‑decay: changes a neutron into a proton (or vice‑versa) and emits an electron or positron

Both processes conserve energy, charge, and the number of nucleons.

Imagine a heavy nucleus as a crowded dance floor. It can “drop” a small, tightly bound pair of dancers (a helium nucleus) to lighten up.

Example:

Decay equation: $$^{238}_{92}\text{U} \;\longrightarrow\; ^{234}_{90}\text{Th} \;+\; ^{4}_{2}\text{He}$$

• Uranium‑238 loses 2 protons and 2 neutrons.
• Thallium‑234 is left with a lower atomic number (Z‑2).
• The emitted helium nucleus is the α‑particle.

🔬 Tip: Remember that the mass number (A) and atomic number (Z) must balance on both sides.

In β‑decay, a neutron in the nucleus “switches” into a proton, emitting an electron (β⁻) and an antineutrino. Think of it as swapping a friend’s identity.

Example:

Decay equation: $$^{14}_{6}\text{C} \;\longrightarrow\; ^{14}_{7}\text{N} \;+\; e^- \;+\; \bar{u}_e$$

• Carbon‑14 (6 protons) becomes Nitrogen‑14 (7 protons).
• One neutron turns into a proton, releasing an electron and an antineutrino.

📚 Exam hint: Check that the charge on the left equals the sum of charges on the right (including the electron’s –1).

Follow these steps to write a correct decay equation:

1. Identify the parent nucleus. Write its symbol, atomic number (Z) and mass number (A).
2. Determine the decay type. α‑decay reduces Z by 2 and A by 4; β⁻‑decay increases Z by 1 and keeps A constant.
3. Write the daughter nucleus. Adjust Z and A accordingly.
4. Add the emitted particle(s). For α‑decay, add $^{4}_{2}\text{He}$; for β⁻‑decay, add $e^-$ and $\bar{u}_e$.
5. Check conservation. Verify that total charge, mass number, and nucleon number balance.

💡 Quick check: The sum of Z on the left equals the sum of Z on the right; the sum of A on the left equals the sum of A on the right.

• 🔍 Read the question carefully. Identify whether it asks for α or β decay.
• 🧮 Use conservation laws. Check charge, mass number, and nucleon number.
• 📝 Show your work. Write intermediate steps; examiners appreciate clear reasoning.
• ⏱️ Time management. Allocate a few minutes to double‑check your equations.
• 📖 Practice with real examples. Work through decay chains of U‑238, Th‑232, and Ra‑226.