3.6 Atomic Model—Rutherford & Niels Bohr models

3.6.1 Rutherford’s Atomic Model (1911)

Rutherford’s atomic model proposes the following structure for an atom:

• Nucleus: The center of the atom contains a positively charged dense core called the nucleus. Protons and neutrons are located inside the nucleus. Since the mass of an electron is negligible compared to the entire atom, the mass and positive charge are determined by the protons and neutrons in the nucleus.

• Size of the Nucleus: The nucleus is very small, and the majority of the atom’s volume is empty space.

• Electron Movement: Electrons move around the nucleus in orbits, similar to how planets orbit the sun in the solar system. The number of electrons is equal to the number of protons, which ensures the atom remains neutral (overall charge = 0).

• Attraction of Electrons to Nucleus: Electrons are attracted to the positively charged nucleus due to a centripetal force, similar to how planets are attracted to the sun, keeping electrons in their orbits.

Rutherford’s Model is often referred to as the solar system model due to its resemblance to the planetary system. It is also called the nuclear model because it was the first to propose the existence of a nucleus.

Limitations of Rutherford’s Model:

Despite being the first widely accepted atomic model, Rutherford’s model has several limitations:

1. Orbit Size and Shape: It does not explain the size or shape of the electron orbits.

2. Electron and Nucleus Charge: The parallel between neutral planets and charged electrons and nuclei is inaccurate.

3. Multiple Electrons: The model doesn’t explain how electrons move when there are multiple electrons in an atom.

4. Energy Emission: According to Maxwell’s electromagnetic theory, a charged particle moving in a circular path emits energy and should spiral inward, eventually collapsing into the nucleus. However, this does not happen in nature, making Rutherford’s model inconsistent with observed behavior.

3.6.2 Bohr’s Atomic Model (1913)

Niels Bohr introduced corrections to Rutherford’s model, leading to Bohr’s atomic model, which addresses some of the previous model’s issues.

Main Postulates of Bohr’s Model:

1. Electron Movement: Electrons move in circular orbits around the nucleus. These orbits are referred to as energy levels, shells, or principal energy levels. Electrons do not absorb or emit energy while moving in these fixed orbits.

• Energy levels are labeled as n = 1, 2, 3, 4, etc. (where n is the principal quantum number).

• Example:

• n = 1 → K shell

• n = 2 → L shell

• n = 3 → M shell

2. Angular Momentum: The angular momentum of an electron in an energy level is given by the equation:

• mvr = nh/2π

• m = mass of the electron (9.11 × 10^-31 kg)

• v = velocity of the electron in the orbit

• r = radius of the orbit

• h = Planck’s constant (6.626 × 10^-34 m·kg/s)

• n = principal quantum number (n = 1, 2, 3, 4,…)

3. Energy Absorption and Emission:

• Electrons absorb energy when they move from a lower energy level to a higher energy level.

• Electrons emit energy when they move from a higher energy level to a lower energy level. The energy emitted or absorbed is given by the equation:

• E = hv (where v is the frequency of the emitted or absorbed light)

• The light emitted by electrons transitioning between energy levels creates an atomic spectrum, observable through a prism.

Bohr’s Model Diagram:

• Shows electrons orbiting the nucleus in discrete, circular orbits (energy levels), with energy absorption or emission occurring during transitions between levels.

Successes of Bohr’s Model:

1. Energy Level Sizes: Bohr’s model specifies the size of energy levels, unlike Rutherford’s model.

2. Energy Absorption and Emission: Bohr’s model correctly explains the absorption and emission of energy when electrons move between energy levels.

3. Atomic Spectra: Bohr’s model successfully explains the atomic spectra of hydrogen (H), a key observation that Rutherford’s model could not.

Limitations of Bohr’s Model:

1. Multi-electron Atoms: Bohr’s model only successfully explains the spectrum of hydrogen (a single-electron atom) and cannot explain the spectra of atoms with more than one electron.

2. Fine Lines in Spectra: Bohr’s model predicts a single line for energy transitions, but experiments show that each line consists of multiple fine lines, which Bohr’s model does not explain.

3. Orbital Shape: Bohr’s model assumes electrons follow circular orbits, but later research showed that electron orbits can also be oval-shaped.

This summary of Rutherford’s and Bohr’s atomic models outlines the key ideas and the improvements Bohr made to Rutherford’s original theory. While Bohr’s model is more accurate, it still has limitations, especially for multi-electron atoms.