All subjects · Physics · WPH14 (Unit 4)

The nuclear atom and alpha scattering

Our picture of the atom changed when alpha particles fired at gold foil bounced back. This lesson covers nuclear notation and the evidence for the nucleus.

Describing nuclei

A nucleus is written as A over Z with the element symbol (for example uranium-235 has A = 235, Z = 92).

Alpha-particle scattering

Geiger and Marsden, working with Rutherford, fired alpha particles at thin gold foil in a vacuum and counted where they went:

How models changed

Each model was replaced when new experimental evidence could not be explained.

Worked example

A 6.0 MeV alpha particle heads straight for a gold nucleus (Z = 79). Find its distance of closest approach.

  1. At closest approach, all E_k has become electric potential energy: E_k = kQq / r.
  2. E_k = 6.0 x 1.60 x 10-13 = 9.6 x 10-13 J
  3. r = 8.99 x 109 x (79 x 1.60 x 10-19)(2 x 1.60 x 10-19) / 9.6 x 10-13

Answer: r = 3.8 x 10-14 m, an upper limit for the radius of the gold nucleus

Key idea: A = protons + neutrons, Z = protons. Most alphas pass straight through (empty space); a few bounce back (tiny, dense, positive nucleus).

Check yourself

  1. How many neutrons are there in a uranium-235 nucleus (Z = 92)?
    Show answer

    143. N = A - Z = 235 - 92 = 143.

  2. A nucleus has nucleon number 40 and contains 22 neutrons. What is its proton number?
    Show answer

    18. Z = A - N = 40 - 22 = 18.

  3. Using the worked example's method, find the closest approach of a 6.0 MeV alpha particle to a gold nucleus (Z = 79), in units of 10-14 m, to 3 s.f.
    Show answer

    3.79 x 10-14 m. r = kQq / E_k = 8.99 x 109 x 1.264 x 10-17 x 3.20 x 10-19 / 9.6 x 10-13 = 3.79 x 10-14 m.

  4. Most alpha particles passed straight through the gold foil. What did this show?
    • Most of the atom is empty space
    • The nucleus is positively charged
    • Electrons are very light
    • Gold atoms are very small
    Show answer

    Most of the atom is empty space. Almost nothing was in the way of most alpha particles.

  5. A very small number of alpha particles were deflected by more than 90°. What did this show?
    • Atoms contain neutrons
    • Alpha particles are negatively charged
    • The positive charge and most of the mass are concentrated in a tiny nucleus
    • Electrons orbit in fixed energy levels
    Show answer

    The positive charge and most of the mass are concentrated in a tiny nucleus. Only a very small, dense, positive region could repel an alpha particle back.

  6. What are isotopes of an element?
    • Nuclei with the same number of protons but different numbers of neutrons
    • Nuclei with the same number of neutrons but different numbers of protons
    • Atoms with different numbers of electrons
    • Nuclei with the same nucleon number
    Show answer

    Nuclei with the same number of protons but different numbers of neutrons. Same element means same Z; different A means different N.

  7. Why was the alpha-scattering experiment done in a vacuum?
    • Gold reacts with air
    • To keep the foil cold
    • Alpha particles have a range of only a few cm in air
    • To stop the alpha particles being deflected by gravity
    Show answer

    Alpha particles have a range of only a few cm in air. Alpha particles are absorbed by air molecules within a few centimetres.

  8. Which model of the atom did the alpha-scattering results replace?
    • The Bohr model
    • The quark model
    • The nuclear model
    • Thomson's plum pudding model
    Show answer

    Thomson's plum pudding model. The plum pudding model has its positive charge spread out, so it cannot deflect alphas through large angles.

Practise with instant feedback

Sources

Last updated 7 November 2026. Spotted a mistake? Tell us.