Why Most of an Atom Is Empty Space

Atoms were long pictured as solid, indivisible balls. Experiments with electricity and radiation showed instead that atoms contain even smaller particles — and that nearly all of an atom's mass is packed into a tiny core, with the rest mostly empty space.

This lesson covers the subatomic particles, Thomson's and Rutherford's models, and atomic number, mass number, isotopes and isobars.

The electron was identified from cathode rays in discharge tubes, the proton from positively charged anode rays, and the neutron as a neutral, penetrating particle given out when beryllium is bombarded with alpha particles.

Electron — cathode rays:

- In a discharge tube at very low pressure and high voltage, rays travel from the cathode to the anode
- They travel in straight lines, cast shadows and bend towards a positive plate, showing they are negatively charged particles
- Their properties do not depend on the gas or the electrode material, so electrons are present in all atoms
- The electron's charge-to-mass ratio is $1.758820\times 10^{11}$ C kg${}^{-1}$, and its charge is $-1.602\times 10^{-19}$ C

Worked example. Dividing the charge by the charge-to-mass ratio gives the electron's mass:

$$m_e=\frac{1.602\times 10^{-19}\text{ C}}{1.758820\times 10^{11}{\text{ C kg}}^{-1}}=9.109\times 10^{-31}\text{ kg}$$

Proton — anode (canal) rays:

- With a perforated cathode, rays moving the opposite way appear behind it
- They are positively charged, and their charge-to-mass ratio depends on the gas in the tube
- The lightest positive particle, from hydrogen gas, is the proton, with charge $+1.602\times 10^{-19}$ C and mass $1.673\times 10^{-27}$ kg

Neutron:

- Bombarding a thin sheet of beryllium with alpha particles releases electrically neutral particles
- Their mass, $1.675\times 10^{-27}$ kg, is slightly greater than that of the proton

An everyday example. A neon sign glowing above a shop works on the same principle as a discharge tube — electricity passing through a gas at low pressure.

The substance. An electron has less than a thousandth of a proton's mass — so electrons add almost nothing to the mass of an atom.

Thomson pictured the atom as a uniform sphere of positive charge with electrons embedded in it, but Rutherford's alpha-particle scattering experiment showed that the positive charge and almost all the mass sit in a tiny nucleus, with electrons moving around it.

Thomson's model:

- A sphere of radius about $10^{-10}$ m with positive charge spread evenly and electrons embedded in it, often compared to a watermelon with its seeds
- It explained why atoms are neutral overall but could not explain the scattering results

Alpha-particle scattering experiment:

- Fast alpha particles were aimed at a very thin gold foil surrounded by a zinc sulphide screen that flashed where each particle struck
- Most alpha particles passed straight through
- A small fraction were deflected through small angles
- Very few bounced almost straight back

Rutherford's nuclear model:

- Most of the atom is empty space
- The positive charge and most of the mass are concentrated in a very small central nucleus, about $10^{-15}$ m across compared with about $10^{-10}$ m for the atom
- Electrons move around the nucleus in circular paths, held by electrostatic attraction

Worked example. The ratio of atomic radius to nuclear radius is

$$\frac{10^{-10}\text{ m}}{10^{-15}\text{ m}}=10^5$$

so if the nucleus were the size of a cricket ball, the atom would be several kilometres across.

Drawbacks. A charged particle moving in a circle should radiate energy and spiral into the nucleus, so the model cannot explain why atoms are stable or how electron energies are arranged.

An everyday example. A gold bangle feels completely solid, yet its atoms are mostly empty space — the electrons of neighbouring atoms keep them apart.

The substance. Thomson's model predicted almost no large deflections — so the few alpha particles that bounced back were what ruled it out.

Atomic number (Z) is the number of protons in the nucleus, mass number (A) is the total number of protons and neutrons, isotopes are atoms of one element with different mass numbers, and isobars are atoms of different elements with the same mass number.

Key relations:

$$\text{Neutrons}=A-Z\text{Electrons in a neutral atom}=Z$$

Notation. An atom is written ${}_Z^A\mathrm{X}$, as in ${}_{17}^{35}\mathrm{Cl}$.

Worked example. For ${}_{17}^{35}\mathrm{Cl}$: protons $=17$, neutrons $=35-17=18$ and electrons $=17$. The chloride ion, $\mathrm{C}{\mathrm{l}}^{-}$, has $17+1=18$ electrons.

Isotopes:

- Same atomic number, different mass numbers, because the number of neutrons differs
- Hydrogen has protium ${}_1^1\mathrm{H}$, deuterium ${}_1^2\mathrm{H}$ and tritium ${}_1^3\mathrm{H}$; carbon has ${}_6^{12}\mathrm{C}$ and ${}_6^{14}\mathrm{C}$
- Isotopes have nearly identical chemical properties, because chemistry depends on electrons

Isobars:

- Different atomic numbers, same mass number, such as ${}_6^{14}\mathrm{C}$ and ${}_7^{14}\mathrm{N}$, or ${}_{18}^{40}\mathrm{Ar}$ and ${}_{20}^{40}\mathrm{Ca}$
- They are different elements, so their chemical properties differ

An everyday example. Radioactive cobalt-60 used for cancer treatment in Indian hospitals is an isotope of ordinary cobalt that differs only in its number of neutrons.

The substance. Isotopes behave alike chemically but differ physically — heavy water, made with deuterium, is denser than ordinary water.