130-131 - Nucleon Number, Proton Number and Alpha Scattering

Counting the nucleus

An atom is mostly empty space, but nearly all of its mass is in the nucleus. To describe a nucleus, physicists count two things very carefully.

The word nucleon means a particle in the nucleus. At this level, the nucleons are protons and neutrons.

So:

Nuclear notation usually places the nucleon number at the upper left and the proton number at the lower left:

$X$ is the chemical symbol. The lower number, $Z$, decides the element because the element is identified by its number of protons.

Worked example:

An atom is written as ${}^{27}_{13}\mathrm{Al}$. Find the numbers of protons, neutrons and nucleons.

Decision point 1: the lower number is not the neutron number. It is the proton number.

Decision point 2: the upper number is the total number of nucleons, not the total number of particles in the whole atom.

Decision point 3: neutrons are found by subtracting the proton number from the nucleon number.

So ${}^{27}_{13}\mathrm{Al}$ has 13 protons, 14 neutrons and 27 nucleons.

For an Edexcel state what is meant by item, be precise. "Mass number is the mass" is too vague. The expected idea is that nucleon number is the total number of protons and neutrons in the nucleus.

Same element, different neutrons

Proton number is the identity label of an element. If two nuclei have the same $Z$, they are the same element even if their neutron numbers differ.

For carbon:

All three are carbon because all three have $Z = 6$. They are different isotopes because they have different neutron numbers.

Misconception contrast: changing the neutron number changes the nucleon number, but it does not change the element. Changing the proton number would change the element because the nucleus would no longer have the same $Z$.

This matters in $\alpha$ scattering too. An $\alpha$ particle is the nucleus of a helium atom, so it can be represented as ${}^{4}_{2}\mathrm{He}$: two protons and two neutrons. Its positive charge is why it is repelled by a positive nucleus, and its relatively large mass compared with an electron is why electron interactions cannot explain large-angle scattering.

Guided check:

Compare ${}^{35}_{17}\mathrm{Cl}$ and ${}^{37}_{17}\mathrm{Cl}$.

1. The proton number is the same: both have 17 protons.
2. The nucleon number is different: 35 and 37.
3. The neutron numbers are different:

So they are isotopes of the same element.

Alpha particles as probes

The $\alpha$-scattering experiment is a probing experiment. A narrow beam of $\alpha$ particles is fired at very thin gold foil, and observers record where the $\alpha$ particles go afterwards.

The key is not one particle. The evidence comes from the pattern after many $\alpha$ particles:

• most pass through with little or no deflection
• some are deflected through small angles
• a very small fraction are turned through very large angles, sometimes back towards the source

[DIAGRAM: asset_name: Alpha-source foil-screen apparatus and non-contact close-approach repulsion causing backscatter; asset_slug: 037_nucleon_proton_number_alpha_scattering__diagram_01; recommended_method: matplotlib; description: Alpha-source foil-screen apparatus and non-contact close-approach repulsion causing backscatter]

Before Rutherford's nuclear model, a tempting picture was that positive charge was spread through the atom, with electrons embedded within it. If the positive charge were spread out like that, each $\alpha$ particle would feel only weak sideways pushes as it passed through. Large-angle scattering would be extremely difficult to explain.

The observations point in a different direction:

Misconception contrast: "the $\alpha$ particles bounced off electrons" sounds plausible because atoms contain electrons. It does not work. Electrons are much less massive than $\alpha$ particles, and their negative charge would attract $\alpha$ particles rather than strongly repel them. Large-angle deflection points to a concentrated positive centre.