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**Advanced Higher Chemistry**

Unit 1 Quantum numbers

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Quantum Numbers Quantum numbers can be used to define the energy of an electron. There are four quantum numbers used: - Principal quantum number (n) - Angular momentum quantum number (ɭ) - Magnetic quantum number (mɭ ) - Spin quantum number (ms)

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**Principal Quantum Number**

The principal quantum number tells you in which electron shell the electron can be found. The electron shells are numbered from nearest the nucleus. The first shell, n = 1, the second shell, n = 2 and so on. The higher the value for n, the higher the potential energy.

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Subshells Emission spectra often contain doublets or triplets of lines. This suggests that the electron shells are further divided. There are four types of subshells: s, p, d and f – sharp, principal, diffuse and fundamental. These subshells have different energies and shapes.

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Subshells Shell Subshell 1 1s 2 2s, 2p 3 3s, 3p, 3d 4 4s, 4p, 4d, 4f

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**Heisenberg’s Uncertainty Principle**

“It is impossible to determine the exact position or momentum of an electron.” The area where there is a high probability (greater than 90%) of finding an electron is known as an atomic orbital.

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**Angular Momentum Quantum Number**

The angular momentum quantum number (l) is used to describe the shape of the orbital within a subshell. It is given the values 0,1,2….(n-1) s orbital : l = 0 p orbital : l = 1 d orbital : l = 2 f orbital : l = 3

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Value of n Value of l Atomic orbital 1 1s 2 2s 2p 3 3s 3p 3d 4 4s 4p 4d 4f

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**Magnetic Quantum Number**

The magnetic quantum number gives the multiplicity and spatial orientation of the orbitals. They can range from – l to + l. s orbital : ml = 0 p orbital : ml = -1, 0, +1 d orbital : ml = -2, -1, 0, +1, +2 f orbital : ml = -3,-2, -1, 0, +1, +2, +3

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s orbitals All s orbitals are spherical and have the angular momentum quantum number 1. As n, the principal quantum number increases, the diameter of the s orbital increases. An s orbital holds two electrons.

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**p orbitals p orbitals are ‘dumb-bell’ shaped.**

They have three magnetic quantum numbers (-1, 0, +1) so there are three orbitals (i.e. can hold 6 electrons). Each orbital is of equal energy (degenerate).

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**d orbitals d orbitals have five values for ml.**

They can hold a total of ten electrons.

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**f orbitals f orbitals are even more complex.**

There are seven of them in each shell. They cannot be represented by diagrams but by mathematical expressions.

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**Spin Quantum Number An electron behaves as if it has spin.**

The spin quantum number can have two values, + ½ or – ½.

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**Pauli Exclusion Principle**

“Each orbital holds a maximum of two electrons with opposing spins.” No two electrons in any one atom can have the same set of quantum numbers. The maximum number of electrons in any one orbital is two. If there are two electrons in an orbital, they have opposing spins.

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**Consider the four quantum numbers of each of the two electrons in the 1s orbital of helium.**

1st electron 2nd electron n = 1 l = 0 ml = 0 ms = +½ ms = -½

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Aufbau Principle All orbitals within a subshell have equal energy (degenerate). These orbitals are filled in order of increasing energy. 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d ………

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**Electronic Configuration**

Increasing energy

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**Hund’s Rule of Maximum Multiplicity**

“When degenerate orbitals are available, electrons fill singly keeping spins parallel before pairing occurs.” The number of parallel spins is maximised.

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