The nucleus

Cambridge·Physics·5.1.2·Extended

Nuclear composition and nuclide notation

An atomic nucleus contains protons and neutrons. Together, these particles are called nucleons. Electrons are found outside the nucleus and are not nucleons.

Protons have relative charge $$+1$$, neutrons have relative charge $$0$$, and electrons have relative charge $$-1$$.

Proton number and nucleon number

The proton number, or atomic number, $$Z$$, is the number of protons in the nucleus. It identifies the element: every atom of a given element has the same proton number.

The nucleon number, or mass number, $$A$$, is the total number of protons and neutrons in the nucleus. Subtracting the number of protons from this total gives the number of neutrons:

number of neutrons=A−Z\text{number of neutrons} = A - Z

Reading nuclide notation

A particular nucleus can be represented using nuclide notation:

ZAX{}^{A}_{Z}\mathrm{X}

Here, $$\mathrm{X}$$ is the element symbol. The upper number, $$A$$, is the nucleon number; the lower number, $$Z$$, is the proton number.

For example, $$ {}^{14}_{6}\mathrm{C} $$ represents a carbon nucleus with 6 protons and 14 nucleons in total. It therefore contains $$14 - 6 = 8$$ neutrons.

Isotopes

Atoms belong to the same element if their nuclei contain the same number of protons. However, atoms of that element can have different numbers of neutrons. These different forms of the same element are called isotopes.

The nucleon number is the total number of protons and neutrons in a nucleus. Isotopes of an element have the same proton number but different neutron numbers, so they also have different nucleon numbers.

For example, carbon-12 and carbon-14 are isotopes of carbon. Both have 6 protons, but carbon-12 has 6 neutrons while carbon-14 has 8. Their nucleon numbers are therefore 12 and 14, respectively.

Nuclear charge and relative mass

A nucleus contains protons and neutrons. Its charge depends on how many protons it contains, while its mass depends mainly on the total number of protons and neutrons.

Nuclear charge

Each proton has a relative charge of $$+1$$. A neutron has no charge, so it does not add to the nuclear charge. The proton number, $$Z$$, is the number of protons in the nucleus. Therefore:

Relative nuclear charge=+Z\text{Relative nuclear charge} = +Z

For example, a nucleus with $$Z = 6$$ has a relative charge of $$+6$$.

Relative nuclear mass

Protons and neutrons are both nucleons. Each has a relative mass of approximately $$1$$. The nucleon number, $$A$$, is the total number of protons and neutrons in the nucleus, so:

Relative nuclear mass≈A\text{Relative nuclear mass} \approx A

For example, a nucleus with six protons and six neutrons has $$A = 12$$ and a relative mass of approximately $$12$$. The mass is not exactly $$A$$: the relative masses of individual nucleons are only approximately $$1$$, and the mass of a bound nucleus differs slightly from the sum of the masses of its separate nucleons.

Nuclear fission

Nuclear fission is the splitting of a heavy nucleus into smaller nuclei. It often occurs after the heavy nucleus absorbs a neutron. The split can also release neutrons.

One possible fission reaction begins when a uranium-235 nucleus absorbs a neutron. It produces barium-141, krypton-92 and three neutrons:

92235U+01n→56141Ba+3692Kr+301n{}^{235}_{92}\mathrm{U}+{}^{1}_{0}\mathrm{n}\rightarrow{}^{141}_{56}\mathrm{Ba}+{}^{92}_{36}\mathrm{Kr}+3{}^{1}_{0}\mathrm{n}

Conservation in the fission equation

In a nuclide equation, the upper number is the nucleon number: the total number of protons and neutrons. The lower number is the proton number. A neutron has nucleon number $$1$$ and proton number $$0$$.

Both totals are conserved in the reaction:

  • Nucleon number: before fission, $$235 + 1 = 236$$; afterwards, $$141 + 92 + 3 = 236$$.
  • Proton number: before fission, $$92 + 0 = 92$$; afterwards, $$56 + 36 = 92$$.

Energy released in fission

Although nucleon number is conserved, the total mass of the products is less than the total mass of the reactants. The mass difference corresponds to the energy released, according to $$E = \Delta m c^2$$, where $$\Delta m$$ is the mass difference and $$c$$ is the speed of light.

Some of the released energy is kinetic energy: the smaller nuclei and neutrons move away from the fission event.

Nuclear fusion

Nuclear fusion is the joining of light atomic nuclei to form a heavier nucleus. A fusion reaction may also produce other particles.

A nuclide equation shows the nuclei and particles involved. The upper number is the nucleon number, the total number of protons and neutrons. The lower number is the proton number, the number of protons.

12H+13H→24He+01n{}^{2}_{1}\mathrm{H}+{}^{3}_{1}\mathrm{H}\rightarrow{}^{4}_{2}\mathrm{He}+{}^{1}_{0}\mathrm{n}

In this reaction, two hydrogen nuclei join to produce a helium nucleus and a neutron. The neutron has one nucleon and no protons.

Both nucleon number and proton number are conserved: their totals are the same before and after the reaction. The total nucleon number is $$2+3=4+1=5$$, and the total proton number is $$1+1=2+0=2$$.

The products have less total mass than the reactants. This mass difference corresponds to energy released in the reaction, including kinetic energy carried by the products.