infer from the results of the α-particle scattering experiment the existence and small size of the nucleus

What are Alpha Particles?

Alpha particles are helium nuclei, consisting of 2 protons and 2 neutrons (\$^{4}_{2}\mathrm{He}\$). They are relatively heavy and carry a +2 charge.

Think of them as tiny “mini‑bombs” that can knock other particles around.

Rutherford’s Gold Foil Experiment

1. Alpha particles were fired at a thin sheet of gold foil.
2. Most particles passed straight through.
3. A few were deflected at large angles, and a few even bounced back.

🔍 Observation: The existence of a tiny, dense, positively charged centre in the atom.

Inferring the Nucleus

Using the Coulomb force between the positively charged alpha particle and the nucleus:

\$F = \frac{1}{4\pi\varepsilon_0}\,\frac{(2e)(Ze)}{r^2}\$

When an alpha particle comes close to the nucleus, the repulsive force can be strong enough to change its direction dramatically.

From the maximum scattering angle (\$\theta_{\text{max}}\$) we can estimate the size of the nucleus:

\$r{\text{nucleus}} \approx \frac{1}{4\pi\varepsilon0}\,\frac{(2e)(Ze)}{E{\alpha}}\tan\left(\frac{\theta{\text{max}}}{2}\right)\$

Result: The nucleus is tiny (≈10⁻¹⁵ m) compared to the whole atom (≈10⁻¹⁰ m).

Analogy: Bowling Ball & Pinball

Imagine a bowling ball (alpha particle) rolling toward a pinball machine (atom). Most of the time it just slides past the machine, but occasionally it hits a heavy pin (nucleus) and gets knocked back or deflected sharply.

Just like the pin is tiny compared to the whole machine, the nucleus is tiny compared to the atom.

Key Points to Remember

• Alpha particles are helium nuclei with a +2 charge.
• Most alpha particles pass through matter; a few are deflected.
• Large deflections imply a small, dense, positively charged centre.
• The nucleus is about 10⁻⁵ times the size of the atom.

Exam Tip: “Explain the significance of the alpha‑particle scattering experiment.”

Use the structure:

1. Describe the experiment setup.
2. State the key observations.
3. Explain how these observations lead to the conclusion about the nucleus.
4. Highlight the size comparison (nucleus vs atom).

Remember to include the Coulomb force equation and the scattering angle formula where relevant.

Quick Practice Question

Suppose an alpha particle with kinetic energy \$E_{\alpha}=5\,\text{MeV}\$ is scattered at an angle of \$90^{\circ}\$. Estimate the radius of the gold nucleus (\$Z=79\$). Use the approximation:

\$r{\text{nucleus}} \approx \frac{1}{4\pi\varepsilon0}\,\frac{(2e)(Ze)}{E_{\alpha}}\$

Show your calculation steps.