Quantum Theory

Bohr Model of Atom Postulate 1: An e- can only have specific energy values, called energy levels.

For a hydrogen atom, the energy associated with each energy level can be found using the formula below.

Hydrogen Energy Level Diagram

Bohr Model of Atom Postulate 2: e- does not radiate energy while occupying an energy level, but gains energy to go to a higher level and radiates energy when falling to a lower energy level.

Movement of electrons The ground state is the low-energy state where you can initially find electrons. When energy is added to the atom, the electrons may use this energy to jump into a higher-energy state called the excited state. The energy of an electron is determined by its average distance from the nucleus. Each atomic orbital with a given set of quantum numbers has a particular energy associated with it, the orbital energy. In atoms or ions that contain only a single electron, all orbitals with the same value of n have the same energy (they are degenerate). Energies of the principal shells increase smoothly as n increases. An atom or ion with the electron(s) in the lowest-energy orbital(s) is said to be in the ground state; an atom or ion in which one or more electrons occupy higher-energy orbitals is said to be in the excited state.

The energy given off when an electron falls from a high energy level to a lower energy level is called electromagnetic radiation. Electromagnetic radiation includes every form of energy that travels in transverse waves: Radio waves - Ultraviolet light Microwaves - X-rays Infrared radiation - Gamma rays Visible light

Quantum Theory The energy of a photon is proportional to its frequency. E = h E: energy (J, joules) h: Planck’s constant (6.626  10-34 J·s) : frequency (Hz, s-1)

Electromagnetic Spectrum Frequency & wavelength are inversely proportional c =  c: speed of light (2.998  108 m/s) : wavelength (m, nm, etc.) : frequency (Hz)

Examples Find the energy of a photon with a frequency of 4.57  1014 Hz. Find the frequency of a wave with wavelength of 3.54 × 10-5 nm. (1 m = 109 nm) Find the energy of a photon with wavelength of 2.85 m.

For the transition of an e- from an initial energy level (Ei) to a final energy level (Ef), we can write

Example: How much energy is released when the electron in a hydrogen atom falls from the 3rd energy level to the 1st energy level? What is the wavelength of the radiation associated with this energy?

Hydrogen Energy Level Diagram

Spectra of Hydrogen