Stable and unstable nuclei

Welcome to the heart of the atom! You already know that the nucleus contains protons and neutrons. But if protons are all positively charged, shouldn't they repel each other and blow the nucleus apart?

In this section, we will answer that question and look at what happens when a nucleus cannot hold itself together.

What you'll learn

• How the strong nuclear force balances electromagnetic repulsion to keep nuclei stable.
• The precise distances over which the strong nuclear force is attractive and repulsive.
• How unstable nuclei decay via alpha and beta emission.
• Why the neutrino had to be invented to save the law of conservation of energy.

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The Strong Nuclear Force

Inside the nucleus, protons experience a massive force of repulsion due to the electromagnetic force. Because they are packed incredibly close together, this repulsive force is huge.

To prevent the nucleus from flying apart, there must be an even stronger attractive force pulling the nucleons (protons and neutrons) together.

The range of the strong nuclear force

The strong nuclear force has a very unusual, complex behaviour depending on the distance between the nucleons. We measure these tiny distances in femtometres. One femtometre ($fm$) is $10^{-15}m$.

1. At extremely short distances (less than $0.5fm$): The strong nuclear force is fiercely repulsive. If it weren't, the nucleons would crush into a single point under their own attraction.
2. At short distances (between roughly $0.5fm$ and $3fm$): The force is highly attractive. This is what binds the nucleus together. The maximum attractive force occurs at roughly $1fm$.
3. At larger distances (beyond $3fm$): The force falls rapidly to zero. It is a strictly short-range force.

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Unstable Nuclei and Alpha Decay

When a nucleus is simply too massive (typically those with more than 82 protons), the strong nuclear force cannot stretch far enough to hold the outer nucleons together against the electromagnetic repulsion. To become more stable, the nucleus emits an alpha particle.

When a parent nucleus emits an alpha particle, it loses 4 from its mass number ($A$) and 2 from its atomic number ($Z$), transmuting into a completely different element. We write the general equation for alpha decay as:

$${}_Z^{A}X{\to }_{Z-2}^{A-4}Y{+}_2^4\alpha$$

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Beta Minus (${\beta }^{-}$) Decay

Sometimes a nucleus isn't necessarily too massive overall, but it has too many neutrons compared to its protons. The strong force balance is wrong. To fix this, a neutron inside the nucleus transforms into a proton, emitting a fast-moving electron called a beta-minus particle.

The general equation for ${\beta }^{-}$ decay requires careful attention to a hidden particle, the antineutrino (${\underset{ˉ}{\nu }}_e$):

$${}_Z^{A}X{\to }_{Z+1}^{A}Y{+}_{-1}^0\beta +{\underset{ˉ}{\nu }}_e$$

The Mystery of the Missing Energy

In the early 20th century, physicists noticed a major problem with beta decay. If a parent nucleus purely split into a daughter nucleus and a beta particle, the rules of momentum and energy conservation dictated that the beta particle should always fly out with exactly the same amount of kinetic energy.

However, experiments showed that beta particles were emitted with a continuous spectrum of energies—anything from near zero up to a maximum value. Some energy appeared to be vanishing!

This ghost particle was named the neutrino (literally "little neutral one"). It had to have zero charge and virtually zero mass, making it incredibly difficult to detect.

Note for A-Level: In ${\beta }^{-}$ decay, the specific particle emitted is an antineutrino (${\underset{ˉ}{\nu }}_e$). The normal neutrino (${\nu }_e$) is emitted in ${\beta }^{+}$ decay (which you will meet later).

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