Electron configuration

The Electromagnetic Spectrum

• The electromagnetic spectrum is a range of frequencies that covers all electromagnetic radiation and their respective wavelengths and energy

• It is divided into bands or regions, and is very important in analytical chemistry.

• The spectrum shows the relationship between frequency, wavelength and energy

• Frequency is how many waves pass per second, and wavelength is the distance between two consecutive peaks on the wave

• Gamma rays, X-rays and UV radiation are all dangerous - you can see from that end of the spectrum that it is high frequency and high energy, which can be very damaging to your health

The electromagnetic spectrum diagram

The electromagnetic spectrum spans a broad spectrum from very long radio waves to very short gamma rays

• All light waves travel at the same speed; what distinguishes them is their different frequencies

• The speed of light (symbol ‘c’) is constant and has a value of 3.00 x 10⁸ ms^-1

• As you can see from the spectrum, frequency (symbol ‘f') is inversely proportional to wavelength (symbol ‘λ')

  • In other words, the higher the frequency, the shorter the wavelength

• The equation that links them is c = fλ 

• Since c is constant you can use the formula to calculate the frequency of radiation given the wavelength, and vice versa

Continuous versus line spectrum

• A continuous spectrum in the visible region contains all the colours of the spectrum

• This is what you are seeing in a rainbow, which is formed by the refraction of white light through a prism or water droplets in rain

Continuous spectrum diagram

A continuous spectrum shows all frequencies of light

• However, a line spectrum only shows certain frequencies

Helium spectrum diagram

The line spectrum of helium which shows only certain frequencies of light

• This tells us that the emitted light from atoms can only be certain fixed frequencies - it is quantised (quanta means 'little packet')

• Electrons can only possess certain amounts of energy - they cannot have any energy value

Examiner Tip

• The formula that relates frequency and wavelength is printed in Section 1 of the IB Chemistry Data Booklet so you don’t need to learn it

• You will also find the speed of light and other useful constants in Section 2

Emission Spectra

• Electrons move rapidly around the nucleus in energy shells

• If their energy is increased, then they can jump to a higher energy level

• The process is reversible, so electrons can return to their original energy levels

  • When this happens, they emit energy

• The frequency of energy is exactly the same, it is just being emitted rather than absorbed:

Absorption and Emission diagram

The difference between absorption and emission depends on whether electrons are jumping from lower to higher energy levels or the other way around

• The energy they emit is a mixture of different frequencies

• This is thought to correspond to the many possibilities of electron jumps between energy shells

• If the emitted energy is in the visible region, it can be analysed by passing it through a diffraction grating

• The result is a line emission spectrum

Line emission spectra

Spectrum of hydrogen diagram

The line emission (visible) spectrum of hydrogen

• Each line is a specific energy value

  • This suggests that electrons can only possess a limited choice of allowed energies

• These packets of energy are called 'quanta' (plural quantum)

• What you should notice about this spectrum is that the lines get closer together towards the blue end of the spectrum

• This is called convergence and the set of lines is converging towards the higher energy end, so the electron is reaching a maximum amount of energy

• This maximum corresponds to the ionisation energy of the electron

• These lines were first observed by the Swiss school teacher Johannes Balmer, and they are named after him

• We now know that these lines correspond to the electron jumping from higher levels down to the second or n = 2 energy level

• A larger version of the hydrogen spectrum from the infrared to the ultraviolet region looks like this

Full hydrogen spectrum diagram

The full hydrogen spectrum

• In the spectrum, we can see sets or families of lines

• Balmer could not explain why the lines were formed - an explanation had to wait until the arrival of Planck's Quantum Theory in 1900

• Niels Bohr applied the Quantum Theory to electrons in 1913, and proposed that electrons could only exist in fixed energy levels

• The line emission spectrum of hydrogen provided evidence of these energy levels and it was deduced that the families of lines corresponded to electrons jumping from higher levels to lower levels

Diagram to show the energy transitions for the hydrogen atom

Electron jumps in the hydrogen spectrum

• The findings helped scientists to understand how electrons work and provided the backbone to our knowledge of energy levels, sublevels and orbitals

• The jumps can be summarised as follows:

Electron Jumps & Energy Table

Worked example

Which electron transition in the hydrogen atom emits visible light?

A. n = 1 to n = 2

B. n = 2 to n = 3

C. n = 2 to n = 1

D. n = 3 to n = 2

Answer

Option D is correct

• Emission in the visible region occurs for an electron jumping from any higher energy level to n = 2

Energy Levels

What are electron shells?

• The arrangement of electrons in an atom is called the electronic configuration

• Electrons are arranged around the nucleus in principal energy levels or principal quantum shells

• Principal quantum numbers (n) are used to number the energy levels or quantum shells

  • The lower the principal quantum number, the closer the shell is to the nucleus

  • The higher the principal quantum number, the greater the energy of the electron within that shell

• Each principal quantum number has a fixed number of electrons it can hold

  • n = 1 : up to 2 electrons

  • n = 2 : up to 8 electrons

  • n = 3 : up to 18 electrons

  • n = 4 : up to 32 electrons

• There is a pattern here - the mathematical relationship between the number of electrons and the principal energy level is 2n² 

  • So for example, in the third shell n = 3 and the number of electrons is 2 x (3²) = 18

 Principle quantum shells

Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbers

What are subshells?

• The principal quantum shells are split into subshells which are given the letters s, p and d

  • Elements with more than 57 electrons also have an f subshell

  • The energy of the electrons in the subshells increases in the order s < p < d

• The order of subshells overlap for the higher principal quantum shells as seen in the diagram below:

Principle Quantum Number and Sub-Shells

Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbers

What are orbitals?

• The subshells contain one or more atomic orbitals

• Orbitals exist at specific energy levels and electrons can only be found at these specific levels, not in between

  • Each atomic orbital can be occupied by a maximum of two electrons

• The orbitals have specific 3D shapes:

The shape of s and p orbitals

Representation of orbitals (the dot represents the nucleus of the atom) showing spherical s orbitals (a), p orbitals containing ‘lobes’ along the x, y and z axis

• Note that the shape of the d orbitals is not required for IB Chemistry

Summary of s and p orbitals

An overview of the shells, subshells and orbitals in an atom

Ground state

• The ground state is the most stable electronic configuration of an atom which has the lowest amount of energy

• This is achieved by filling the subshells of energy with the lowest energy first (1s)

  • This is called the Aufbau Principle

• The order of the subshells in terms of increasing energy does not follow a regular pattern at n = 3 and higher

The Aufbau Principle

The Aufbau Principle - following the arrows gives you the filling order

Sublevels & Orbitals

• The principal quantum shells increase in energy with increasing principal quantum number

  • E.g. n = 4 is higher in energy than n = 2

• The subshells increase in energy as follows: s ＜ p ＜ d ＜ f

  • The only exception to these rules is the 3d orbital which has slightly higher energy than the 4s orbital, so the 4s orbital is filled before the 3d orbital

Energy Levels

Relative energies of the shells and subshells

• Each shell can be divided further into subshells, labelled s, p, d and f

• Each subshell can hold a specific number of orbitals:

  • s subshell : 1 orbital

  • p subshell : 3 orbitals labelled p_x, p_y and p_z

  • d subshell : 5 orbitals

  • f subshell : 7 orbitals

• Each orbital can hold a maximum number of 2 electrons so the maximum number of electrons in each subshell is as follows:

  • s : 1 x 2 = total of 2 electrons

  • p : 3 x 2 = total of 6 electrons

  • d : 5 x 2 = total of 10 electrons

  • f : 7 x 2 = total of 14 electrons

• In the ground state, orbitals in the same subshell have the same energy and are said to be degenerate, so the energy of a px orbital is the same as a p_y orbital

Division of Shells Diagram

Shells are divided into subshells which are further divided into orbitals

Summary of the Arrangement of Electrons in Atoms Table

What is the shape of an s orbital?

• The s orbitals are spherical in shape

• The size of the s orbitals increases with increasing shell number

  • E.g. the s orbital of the third quantum shell (n = 3) is bigger than the s orbital of the first quantum shell (n = 1)

s orbital diagram

The s orbitals become larger with increasing principal quantum number

What is the shape of a p orbital?

• The p orbitals are dumbbell-shaped

• Every shell has three p orbitals except for the first one (n = 1)

• The p orbitals occupy the x, y and z axes and point at right angles to each other, so are oriented perpendicular to one another

• The lobes of the p orbitals become larger and longer with increasing shell number

p orbital diagram

The p orbitals become larger and longer with increasing principal quantum number