1. The Bohr Model of the Atom

2. The behavior of electrons in atoms is revealed by the light given off when the electrons are “excited” (made to absorb energy).

4. Johann Balmer showed that the visible series of lines from the hydrogen spectrum obeyed the formula:

5. Niels Bohr explained all the various lines by proposing that electrons in atoms could have only certain energies, and that light was given off when an electron underwent a transition from a higher energy level to a lower one. This leads to the following picture of what is happening:

7. Bohr derived a more general formula to predict the observed energies of light: Each electron’s energy is determined by which level it is in. The levels are designated by whole numbers, n. Then for a change from one level to another, the energy difference can be calculated: The energy cannot take any value, but has only certain values depending on n.

8. What is frequency of light emitted from an electron undergoing a transition from the n = 3 to the n = 2 level in the hydrogen atom?

9. Find the frequency of this light: Find the wavelength of this light:

10. Now, for what really happens... For atoms with >1 electron, we must use a more complete theory. This theory, known as quantum mechanics, has more quantum numbers than just n. Each electron is characterized by n, and three other quantum numbers.

11. Here are the quantum numbers, and the values they can take: n = 1, 2, 3... (Principal quantum number) l = 0, 1, 2... (n – 1) (Angular momentum quantum number) (Determines shape of orbit ) m l = - l.... + l (Magnetic quantum number) (Determines orientation) m s = +½ or -½ (Spin quantum number)

12. The energy and location of each electron in an atom is determined by these numbers. Each electron has one set: {n, l, m l, m s }. Pauli exclusion principle: Each electron in an atom must have a unique set of the four quantum numbers.