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 m l ). 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) m l = describe orbital’s orientation in space (magnetic quantum number). m s = 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 m l =0. The electrons can spin in either direction around its axis so the possible m s 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 m l =0 but the p orbitals have electrons in 3 different orientations so m l =-1, 0, 1. Each electron can spin in either direction around its axis so the possible m s values are +1/2 and -1/2. Each electron can only have 1 m s 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 2 nd 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.