Chapter 29 Atomic Physics

Early Models of the Atom – Rutherford Planetary model Based on results of thin foil experiments Positive charge is concentrated in the center of the atom, called the nucleus Electrons orbit the nucleus like planets orbit the sun

The trouble with the atom Maxwell’s equations says that all accelerating charge must radiate. As electrons orbits the nucleus it must also radiates continuously, hence losing energy. Result: The electron theoretically should spiral into the nucleus in a very short time (10-8s)… and we should all be dead.

The Bohr Theory of Hydrogen In 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theory His model includes both classical and non-classical ideas He applied Planck’s ideas of quantized energy levels to orbiting electrons In this model, the electrons are generally confined to stable, non-radiating orbits called stationary states

Energy levels Bohr’s work lead to the prediction of the existence of energy levels inside atoms. The energy of an electron when measured must lie in one of the levels, it can never possess energy between two levels. In other words, the energy between the levels are forbidden. In particular, it predicts the existence of the ground state (the lowest energy level). No energy level lies below the ground state. This prevents the decay of the electron orbit because it cannot drop below the ground state. For hydrogen:

End of Lecture 11/14

Terminology Ground state: n =1 First excited state: n =2 Second excited state: n =3 Ionization energy: The energy required to free an electron = E∞-E1 For hydrogen, the ionization energy is: E∞-E1 = 0 - (-13.6eV) = 13.6eV

Energy transition of electron

Emitting a photon Find the frequency of the photon emitted when an electron drops from n=5 to n=2.

Find the wavelength and frequency for the following transitions (n given): λ

Single electron ions other than hydrogen

Atomic spectrum

Electron Spin

Quantum Numbers inside an atom

Shells Historically, all states having the same principle quantum number n are said to form a shell Shells are identified by letters K, L, M … All states having the same values of n and l are said to form a subshell (orbital) The letters s, p,d, f, g, h, ... are used to designate the subshells for which l = 0, 1, 2, 3, …

Terminology n 1 2 3 4 5 Name K L M N O

Terminology l 1 2 3 4 5 Name s p d f g h 1 2 3 4 5 Name s p d f g h For example, if there are 2 electrons in the n =1, l =0 orbital, 2 electrons in the n =2, l =0 orbital, 4 electrons in the n =2, l =1 orbital, we write: 1s2 2s2 2p4 Historical names: s: sharp, p: principle, d: diffuised, f: fundamental

Shell and Subshell Notation Summary

For each l ,how many states are there?

Calculate the maximum number of electrons in the s, p, d, f, g orbitals.

Example Find all possible wave functions for an electron with n=1. Then do the same for n=2 and n=3.

Periodic Table, cont By noting the columns in which some missing elements should be located, chemists were able to make rough predictions about their chemical properties Within 20 years of the predictions, most of the elements were discovered The elements in the periodic table are arranged so that all those in a column have similar chemical properties

Periodic Table, Explained The chemical behavior of an element depends on the outermost shell that contains electrons For example, the inert gases (last column) have filled subshells and a wide energy gap occurs between the filled shell and the next available shell

Atomic number, Z The atomic number, Z, indicates how many protons there are in the nucleus. Recall that each proton carries charge of +e. If the atom is neutral, it means there must be exactly Z electrons orbiting the nucleus.

Fill the energy from the bottom Each box can fit two electrons, one up, one down.

H and He

Li and Be

B and C

N and O

F and Ne

Animation

Summary

Write down the electron configuration of 6C Now you do the same for 10Ne, 11Na, and 17Cl. Complete shells are more stable than incomplete shells. Cl needs one more e to be complete, and Na has one e too many. Na can give e to Cl to form stable NaCl compound (table salt).

What about 26Fe? It turns out that 4s orbital has a lower energy than the 3d orbital, so the electrons will fill up 4s first before occupying 3s.

The Pauli Exclusion Principle Why can’t we stuff more electrons into each orbital? Electrons cannot occupy the same state (i.e., no two electrons can have exactly the same set of quantum numbers). Once all the states in an orbital are taken, the next electrons have to pick a higher energy level. E.g. Going to a concert with tickets.