Bohr Model & Energy Levels

Understanding the Bohr Model

The Bohr Model of the atom was proposed by Niels Bohr in 1913. It describes the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus.

• Quantized Orbits: Electrons can only occupy certain allowed orbits, each with a specific energy level.
• Energy Levels: The energy of an electron in an orbit is quantized, meaning it can only have certain values.
• Transitions: Electrons can jump from one energy level to another, absorbing or emitting a photon with energy equal to the difference between the levels.

Energy Levels in Atoms

In the Bohr model, energy levels are represented by the principal quantum number, n. The energy of an electron in a particular orbit is given by:

$$E_n = - \frac{13.6 \text{ eV}}{n^2}$$

• Ground State: The lowest energy level (n=1) is called the ground state.
• Excited States: Higher energy levels (n=2, 3, ...) are called excited states.
• Energy Difference: The energy difference between levels determines the frequency of light absorbed or emitted.

Example: Hydrogen Atom

For a hydrogen atom, the energy levels are calculated using the formula:

$$E_n = - \frac{13.6 \text{ eV}}{n^2}$$

For example, the energy of the first excited state (n=2) is:

$$E_2 = - \frac{13.6 \text{ eV}}{2^2} = -3.4 \text{ eV}$$