section 3.2 – page 174. de broglie proposed the dual nature of light; it could act as a particle...

THE QUANTUM MECHANICAL MODEL OF THE ATOM

Section 3.2 – page 174

De Broglie

Proposed the dual nature of light; it could act as a particle or a wave.

Schrodinger

Published the wave equation. Determined the quantum numbers

(n, l and ml). The model of the atom where

electrons are treated as waves is referred to as the Quantum Mechanical Model.

Born

Showed that wave functions (based on the wave equation) could be used to determine the probability of finding an electron at any point within the region of space described by the wave function.

Heisenberg

Showed that it is impossible to know both the position and momentum of a particle with precision – Heisenberg Uncertainly Principle.

Hence, we can picture the electrons like a cloud around the nucleus.

Higher density of the cloud = higher probability of finding an electron in that location.

Summary

Motion of electron around nucleus described by wave equation (same as waves in a fluid).

The solution to the wave equation is a wave function.

If we could determine the wave function for every electron in an atom, we would have a complete “picture” of the atom.

BUT…wave equations are so complex, this is impossible! We can only approximate by predicting.

Quantum Mechanical Model

Electrons belong to different layers, or shells at different distances from the nucleus.

The farther a shell is, the more electrons it can hold and the greater the energy of the electrons.

Within each shell, electrons are grouped in pairs into regions of space called orbitals – the space where an electron spends 90-95% of its time.

Orbitals can have different shapes depending on the energy level to which it belongs.

Each orbital can be described mathematically by its wave function.

There are four kinds of orbitals: s, p, f, d.

Quantum Numbers

Describe specific properties of electrons in atoms.

n = principle quantum number = orbital’s energy level and relative size

l = describe orbital’s shape (subshell)

ml = describe orbital’s orientation in space (magnetic quantum number).

ms= describes behaviour of a specific electron in an orbital (spin quantum number).

Describing Atomic Structure using Quantum Numbers If an atom has n=1, what are the possible

atomic structures? How many are possible? n=1 means electrons exist ONLY in the first energy

level. Therefore, there is only one possible shape, so l=0.

This is the spherical shape (s orbital). Electrons in the l=0 (s orbital), only have 1

orientation therefore ml=0. The electrons can spin in either direction around its

axis so the possible ms values are +1/2 and -1/2. In this case, there are only 2 different atomic

structures because only 2 electrons can exist in the first energy level.

If an atom has n=2, what are the possible atomic structures? How many are possible? n=2 means electrons are in the first AND second

energy level. Therefore, there are 2 possible orbital shapes

(sublevels), l=0 (s) and l=1 (p). The s-orbital only has electrons in 1 orientation so

ml=0 but the p orbitals have electrons in 3 different orientations so ml=-1, 0, 1.

Each electron can spin in either direction around its axis so the possible ms values are +1/2 and -1/2. Each electron can only have 1 ms value and paired electrons must have opposite spins.

In this case there are 8 possible electron configurations for n=2 (similar to how there are only 8 electrons allowed in the 2nd energy level). 2 electrons possible in the 2s orbital 6 electrons possible in the p orbitals (2

electrons in each of the 3 orientations.)

Pauli Exclusion Principle

2 electrons can exist in an orbital. They must be of opposite spins

(+1/2, -1/2) So, no 2 electrons in an atom have

the same 4 quantum numbers.

Textbook

Reading – pages 174-178 Practice – page 179 - #1-10