Advanced Higher Advanced Higher ChemistryChemistry

Unit 1 Unit 1

Quantum numbersQuantum numbers

Quantum NumbersQuantum Numbers

• Quantum numbers can be used to Quantum numbers can be used to define the energy of an electron.define the energy of an electron.

• There are four quantum numbers used:There are four quantum numbers used:

- Principal quantum number (n)- Principal quantum number (n)

- Angular momentum quantum number - Angular momentum quantum number ((ɭɭ) )

- Magnetic quantum number- Magnetic quantum number (m(mɭ ɭ ))

- Spin quantum number (m- Spin quantum number (mss))

Principal Quantum NumberPrincipal Quantum Number

• The principal quantum number The principal quantum number tells you in which electron shell the tells you in which electron shell the electron can be found.electron can be found.

• The electron shells are numbered The electron shells are numbered from nearest the nucleus.from nearest the nucleus.

• The first shell, n = 1, the second The first shell, n = 1, the second shell, n = 2 and so on.shell, n = 2 and so on.

• The higher the value for n, the The higher the value for n, the higher the potential energy.higher the potential energy.

Subshells Subshells

• Emission spectra often contain doublets Emission spectra often contain doublets or triplets of lines.or triplets of lines.

• This suggests that the electron shells This suggests that the electron shells are further divided.are further divided.

• There are four types of subshells:There are four types of subshells:s, p, d and f – sharp, principal, diffuse s, p, d and f – sharp, principal, diffuse and fundamental.and fundamental.

• These subshells have different energies These subshells have different energies and shapes.and shapes.

Subshells Subshells

Shell Shell Subshell Subshell

11 1s1s

22 2s, 2p2s, 2p

33 3s, 3p, 3d3s, 3p, 3d

44 4s, 4p, 4d, 4f4s, 4p, 4d, 4f

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

• ““It is impossible to determine the It is impossible to determine the exact position or momentum of an exact position or momentum of an electron.”electron.”

• The area where there is a high The area where there is a high probability (greater than 90%) of probability (greater than 90%) of finding an electron is known as an finding an electron is known as an atomic orbital.atomic orbital.

Angular Momentum Angular Momentum Quantum NumberQuantum Number

• The angular momentum quantum The angular momentum quantum number (l) is used to describe the number (l) is used to describe the shape of the orbital within a shape of the orbital within a subshell. It is given the values subshell. It is given the values 0,1,2….(n-1)0,1,2….(n-1)

• s orbital : l = 0s orbital : l = 0• p orbital : l = 1p orbital : l = 1• d orbital : l = 2d orbital : l = 2• f orbital : l = 3f orbital : l = 3

Value of nValue of n Value of lValue of l Atomic Atomic orbitalorbital

11 00 1s1s

22 00

112s2s

2p2p

33 00

11

22

3s3s

3p3p

3d3d

44 00

11

22

33

4s4s

4p4p

4d4d

4f4f

Magnetic Quantum Magnetic Quantum NumberNumber

• The magnetic quantum number gives The magnetic quantum number gives the multiplicity and spatial orientation the multiplicity and spatial orientation of the orbitals.of the orbitals.

• They can range from – They can range from – ll to + to + ll..• s orbital : ms orbital : mll = 0 = 0• p orbital : mp orbital : mll = -1, 0, +1 = -1, 0, +1• d orbital : md orbital : mll = -2, -1, 0, +1, +2 = -2, -1, 0, +1, +2• f orbitalf orbital : m : mll = -3,-2, -1, 0, +1, +2, +3 = -3,-2, -1, 0, +1, +2, +3

s orbitalss orbitals• All s orbitals are spherical and All s orbitals are spherical and

have the angular momentum have the angular momentum quantum number 1.quantum number 1.

• As n, the principal quantum As n, the principal quantum number increases, the diameter of number increases, the diameter of the s orbital increases.the s orbital increases.

• An s orbital holds two electrons.An s orbital holds two electrons.

p orbitalsp orbitals• p orbitals are ‘dumb-bell’ shaped.p orbitals are ‘dumb-bell’ shaped.• They have three magnetic They have three magnetic

quantum numbers (-1, 0, +1) so quantum numbers (-1, 0, +1) so there are three orbitals (i.e. can there are three orbitals (i.e. can hold 6 electrons).hold 6 electrons).

• Each orbital is of equal energy Each orbital is of equal energy (degenerate).(degenerate).

d orbitalsd orbitals

• d orbitals have five values for md orbitals have five values for mll..

• They can hold a total of ten They can hold a total of ten electrons.electrons.

f orbitalsf orbitals

f orbitals are even more complex.f orbitals are even more complex. There are seven of them in each There are seven of them in each

shell.shell. They cannot be represented by They cannot be represented by

diagrams but by mathematical diagrams but by mathematical expressions.expressions.

Spin Quantum NumberSpin Quantum Number

• An electron behaves as if it has An electron behaves as if it has spin.spin.

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

Pauli Exclusion PrinciplePauli Exclusion Principle

• ““Each orbital holds a maximum of Each orbital holds a maximum of two electrons with opposing spins.”two electrons with opposing spins.”

• No two electrons in any one atom No two electrons in any one atom can have the same set of quantum can have the same set of quantum numbers.numbers.

• The maximum number of electrons The maximum number of electrons in any one orbital is two.in any one orbital is two.

• If there are two electrons in an If there are two electrons in an orbital, they have opposing spins.orbital, they have opposing spins.

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

11stst electronelectron

22ndnd electronelectron

n = 1n = 1 n = 1n = 1

l = 0l = 0 l = 0l = 0

mmll = 0 = 0 mmll = 0 = 0

mmss = + = +½½ mmss = - = -½½

Aufbau PrincipleAufbau Principle

• All orbitals within a subshell have All orbitals within a subshell have equal energy (degenerate).equal energy (degenerate).

• These orbitals are filled in order of These orbitals are filled in order of increasing energy.increasing energy.

• 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d ………1s 2s 2p 3s 3p 4s 3d 4p 5s 4d ………

Electronic ConfigurationElectronic Configuration

Increasing Increasing energyenergy

Hund’s Rule of Maximum Hund’s Rule of Maximum MultiplicityMultiplicity

• ““When degenerate orbitals are When degenerate orbitals are available, electrons fill singly available, electrons fill singly keeping spins parallel before keeping spins parallel before pairing occurs.”pairing occurs.”

• The number of parallel spins is The number of parallel spins is maximised.maximised.