Revise electric charge, Coulomb's law, superposition, electric fields, field lines, flux and Gauss's law through concise explanations, formulas and chapter-focused summaries.
An atom consists of a positively charged nucleus surrounded by negatively charged electrons. Different atomic models were proposed to explain how these particles are arranged and why atoms remain stable.
J. J. Thomson proposed that an atom was a positively charged sphere with electrons embedded in it. This model explained the electrical neutrality of an atom but could not explain the results of alpha-particle scattering experiments.
Rutherford and his colleagues directed alpha particles at a thin gold foil. Most particles passed through without deflection, some were deflected through small angles, and a very small number returned backwards.
These observations led Rutherford to conclude that most of an atom is empty space. Almost all its positive charge and mass are concentrated in a very small central nucleus. Electrons revolve around this nucleus.
The model could not explain atomic stability. According to classical electromagnetic theory, an accelerating charged particle should continuously radiate energy. A revolving electron should therefore lose energy, move towards the nucleus and eventually collapse into it. Real atoms do not behave this way.
Niels Bohr modified Rutherford's model by introducing quantised electron orbits. His model was based on the following postulates:
mvr = nh/2?, where n = 1, 2, 3...h? = |E2 ? E1|.The integer n is called the principal quantum number. The orbit with n = 1 has the lowest energy and is known as the ground state. Orbits with higher values of n represent excited states.
For a hydrogen-like atom containing one electron and a nucleus of atomic number Z, the radius of the nth permitted orbit is:
rn = n^2a0/Z
Here, a0 = 0.529 angstrom is the Bohr radius. The radius increases with the square of the principal quantum number.
The energy of an electron in the nth orbit is:
En = ?13.6Z^2/n^2 eV
The negative sign indicates that the electron is bound to the nucleus. As n increases, the energy becomes less negative and approaches zero. At zero energy, the electron is free from the atom.
When an excited hydrogen atom returns to a lower energy state, it emits a photon of a definite frequency. Because only specific energy levels are allowed, hydrogen produces a line spectrum rather than a continuous spectrum.
The wavelength of an emitted spectral line is calculated using the Rydberg formula:
1/? = RZ^2(1/n1^2 ? 1/n2^2), where n2 > n1.
n = 1; ultraviolet region.n = 2; mainly visible region.n = 3; infrared region.n = 4; infrared region.n = 5; infrared region.Excitation occurs when an electron absorbs energy and moves from a lower orbit to a higher permitted orbit. Excitation energy equals the difference between the two energy levels.
Ionisation occurs when sufficient energy is supplied to remove the electron completely from the atom. For hydrogen in its ground state, the ionisation energy is 13.6 eV.
| Basis | Excitation | Ionisation |
|---|---|---|
| Meaning | An electron moves from a lower energy level to a higher energy level. | An electron is completely removed from the atom. |
| Final state | The electron remains bound to the atom. | The electron becomes free and the atom becomes an ion. |
| Energy required | Less than the ionisation energy for the same initial state. | Equal to or greater than the ionisation energy. |
Bohr's model successfully explains the stability and spectrum of hydrogen and hydrogen-like ions. However, it cannot accurately explain atoms containing several electrons, the fine structure of spectral lines, their relative intensities, or splitting caused by electric and magnetic fields. It is also inconsistent with the complete wave nature of electrons and the uncertainty principle.
n that identifies an electron's energy level.mvr = nh/2?rn = n^2a0/ZEn = ?13.6Z^2/n^2 eVh? = |E2 ? E1|1/? = RZ^2(1/n1^2 ? 1/n2^2)E = hc/?0.529 angstrom.1.097 x 10? m?^1.These notes bring together the main ideas from Electric Charges and Fields, including electric charge, Coulomb's law, superposition, electric fields, field lines, flux and Gauss's law. Definitions, relationships and formulas are presented in a compact sequence so students can reconnect each result with the concept behind it. Use the notes after reading the chapter, while solving examples, or during final revision. They are designed to improve recall and clarify the chapter structure, while diagrams, derivations and numerical methods should still be practised separately wherever the textbook or examination requires them.