Bohr Model of the Atom

Rutherford's Atomic Paradox: Classical physics predicted electrons orbiting a positive nucleus would continuously emit electromagnetic radiation and spiral into the nucleus.
Bohr's Postulates (1913):
- Electrons orbit the nucleus only in specific circular orbits with specific, allowed energies.
- The hydrogen atom does not emit energy while the electron is in one of these fixed orbits.
- An electron moves to a different orbit only by emitting or absorbing a photon with energy equal to the difference in energy between the two orbits.

Energy Equation: The energies of electron orbits in hydrogen are given by:
- E_n = -\frac{k}{n^2}
- Where k = 2.18 \times 10^{-18} \text{ J} is a constant, and n is the principal quantum number (orbit number).
Significance of Negative Energy: The negative sign indicates that the electron's zero energy point is when it is completely removed from the nucleus (n \to \infty).
Energy Levels: More negative energy means lower energy. The n=1 orbit has the lowest energy (ground state). As n increases, the electron's energy and distance from the nucleus increase.

Ground State: The lowest energy level, typically where the electron resides (n=1).
Excited State: A higher energy level reached when the atom absorbs energy and the electron moves to a higher n orbit.
Energy Change for Transitions: The energy change for an electron transition is:
- \Delta E = -k \left( \frac{1}{n{\text{final}}^2} - \frac{1}{n{\text{initial}}^2} \right)
- When energy is absorbed (n{\text{initial}} < n{\text{final}}), \Delta E is positive.
- When energy is emitted (n{\text{initial}} > n{\text{final}}), \Delta E is negative (e.g., electron moves from excited state back to ground state).
Photon Properties: The energy of the corresponding photon is equal to the magnitude of \Delta E (E_{\text{photon}} = |\Delta E|).
- Photon frequency (\nu) and wavelength (\lambda) can be calculated using E_{\text{photon}} = h\nu and \lambda\nu = c.