# Atomic Structure

The particles from which atoms are made are protons, neutrons and electrons.

Properties:    Particle                      Mass                    Charge

electron                     1/2000th unit          -1

proton                        1 unit                         +1

neutron                      1 unit                          0 The nucleus (containing the protons & neutrons) has an overall positive charge, and the electrons orbiting around it are negatively charged, so an atom has charge distribution – positive in the middle and negative surrounding this region.

Most of an atom is empty space – protons, neutrons and electrons are very small compared to atoms, but because protons and neutrons weigh much more than electrons, virtually all the mass in an atom is in the nucleus.

### Numbers of protons, neutrons and electrons

Protons

The number of protons in an atom is the atomic number. The periodic table is arranged in order of increasing atomic number – each different type of atom is identified by its unique number of protons.
Neutrons

The total number of protons and neutrons (nucleons) in an atom is the mass number. Therefore   number of neutrons = mass number – atomic number

Electrons

Because an atom has no overall charge, there must be exactly the same number of electrons as protons in an atom.

While atoms do not lose or gain protons or neutrons, they can lose or gain electrons to become ions with an overall charge. An ion with a positive charge has lost electrons (there are now more protons than electrons). The magnitude of the charge indicates the number of electrons that have been lost. An ion with a negative charge has gained electrons – again the magnitude of the charge indicates how many electrons have been gained.

Application

What is the number of protons, neutrons and electrons in an atom of scandium-45?

```Protons =  21 (look it up on periodic table)
Neutrons = 45-21 = 24   (given mass number - number of protons)
Electrons = 21  (equal to number of protons for an atom)```

What is the number of  protons, neutrons and electrons in an Sc3+ ion of the same isotope?

```  Protons = 21  (it is still scandium)
Neutrons = 45-21=24  (it is the same isotope)
Electrons = 21-3 = 18  (a 3+ ion means 3 electrons have been lost)```

Give the identity of a particle with 53 protons, 74 neutrons and 54 electrons:

```  Protons = 53  which is the atomic number of iodine
Protons + neutrons = 53 + 74 = 127 so isotope is iodine-127
One more electron than protons so an ion with a 1- charge:   127I -```

### Isotopes

Definition: Isotopes of an element have the same number of protons (same atomic number) but different numbers of neutrons.

Because they have the same electronic structure, isotopes of an element have the same chemical properties, but they have different physical properties – most notably different masses.

### Relative Masses

We need a scale to be able to compare masses of atoms, so we need a standard – a fixed value to compare to. The standard is chosen to be an atom of the isotope carbon-12. We define this as having a mass of exactly 12, then compare the masses of other atoms relative to this – so we call the masses we work out relative masses.

The mass of any individual atom is given by its relative isotopic mass.

Definition: The relative isotopic mass is the mass of an atom of an isotope of an element compared with 1/12 the mass of an atom of carbon-12.

Most elements we encounter are a mixture of all the naturally-occurring isotopes. The relative abundance of each isotope tells us what percentage of each isotope is present. When dealing with such a mixture of isotopes, we need to know the average mass of an atom in the mixture. The is the relative atomic mass.

Definition:      The relative atomic mass is the weighted mean mass of an atom of an element, compared with 1/12 of the mass of an atom of carbon-12

Symbol:        Ar

The ‘weighted mean mass’ means the average mass of an atom, taking into account all the isotopes present and the proportions of each isotope.

### Measurement of relative atomic masses and relative abundances

We measure the mass of atoms accurately using a mass spectrometer. The output from a mass spectrometer tells us the relative isotopic mass of each isotope present, and the abundance of that isotope. Principle: The gaseous sample is atomised by a high energy electron beam.This also removes an electron from some atoms. These positively charged ions are accelerated in an electric field, then deflected by a magnetic field at 90º to their flight path. The lighter they are, the more they are deflected, so the mass spectrometer separates the ions on the basis of their mass. The strength of the detector signal for each different angle of deflection is a measure of the abundance of ions of that specific isotopic mass.

Units:  The x-axis is labelled m/z, (or m/e) which means mass/charge. The ions all have +1 charge, so this is effectively a mass axis. The mass spectrometer is calibrated so that the carbon-12 isotope is given an m/z of exactly 12, so the mass spectrometer measures the relative isotopic mass of the ions directly.

The y-axis is abundance, showing the proportion of ions from the sample which have each different mass. These might be expressed as percentages (relative abundance) or as fractions (fractional abundance) – in either case the relative abundances of all the isotopes must add up to 100%, or the fractional abundances to 1. The results are used to calculate the Ar:

Ar = Σ (fractional abundance for each isotope x relative isotopic mass of that isotope)

The method for working out the Ar value is:

1. multiply each fractional abundance by the mass of that isotope
2. add the results of these multiplications to get the relative atomic mass

Application

Mass spectrometry shows that a sample of Br has two isotopes; 79Br and 81Br. Their abundances are 50.52% and 49.48% respectively. Show that the RAM of bromine in this sample is 79.99 to 4 significant figures.

```Isotope     rel ab.     frac. ab.     rel iso mass x frac abundance
79Br         50.52       0.5052       79 x 0.5052   = 39.9108
81Br         49.48       0.4948       81 x 0.4948   = 40.0788

Ar         = 79.9896
= 79.99 (to 4sig figs)```

### Relative Formula Mass

Now we know the masses of atoms, we can use them to calculate masses of molecules, (relative molecular mass, Mr) by adding the masses of the atoms given in the molecular formula.

Not everything is formed of simple molecules (i.e. substances with giant structures) but these have an empirical formula, so more generally the relative formula mass is the sum of the relative atomic masses in the formula unit. e.g. one formula unit of Ca(OH)2 is one Ca2+ and two OH ions.

Units:     In all these cases, there are NO UNITS – we’re comparing to a unit-less scale.

Application

Determine the relative formula masses of the following compounds:  i) sodium chloride, ii) sodium hydroxide, iii) nickel(II) sulphate(VI), iv) aluminium hydroxide.

``` i)          NaCl       Mr =       23 + 35.5                = 58.5
ii)         NaOH       Mr =      23 + 16 + 1               = 40
iii)        NiSO4      Mr =       58.7 + 32.1 + (4 x 16)   = 154.8
iv)        Al(OH)­3     Mr =      27 + ((16 + 1) x 3)       = 78
```

### Moles

Atoms combine in fixed proportions when they react. For example, 24.3g of magnesium will react with exactly 16.0g of oxygen to form magnesium oxide. This is because there the same number of magnesium atoms in 24.3g of magnesium as there are oxygen atoms in 16g of oxygen, and they are combining in a 1:1 ratio since the empirical formula of magnesium oxide is MgO.

We call this number of atoms one mole (symbol ‘mol’). The mole is the unit of measurement of ‘amount of substance’. The Avogadro constant, having a value of        6.02 x 1023 mol-1 and symbol NA, is the actual number of atoms, ions or molecules in a mole of atoms, ions or molecules.

Definition:     The mole is the mass of an element or compound that contains exactly the same number of particles as there are atoms in 12g of carbon-12    (i.e. 6.02 x 1023 particles)

Application
39.9g of argon contains 6.02 x 1023 Ar atoms
18g of water contains 6.02 x 1023 H2O molecules
2g of hydrogen contains 6.02 x 1023 H2 molecules  (12.04 x 1023 H atoms)

When we write balanced equations, the numbers in front (properly called the stoichiometry), are numbers of moles.

As a consequence of using 12g of carbon-12 as the standard, to obtain one mole of a substance, we must weigh out the Mr in grams.

### Molar Mass:

We sometimes refer to the molar mass of a substance. The units are grams per mole          (g mol-1)

```e.g.    a mole of magnesium weighs 24.3g              both of these mean
the molar mass of magnesium is 24.3 g mol-1    the same thing```

### Converting between mass and moles The equations we need are               MOLES = MASS (g) ÷ Mr

MASS (g) = MOLES × Mr

Mr = MASS (g) ÷ MOLES

Application

1. How many moles of water is 2.7g of water? (Mr of H2O = 18.0)
2. What is the mass of 2.5 moles of sulphur atoms?
3. 0.3 moles of a gas A has a mass of 8.4g. Calculate the molar mass of the gas, and suggest its identity.
```1. Use Moles = Mass ÷ Mr      Moles = 2.7 / 18.0  = 0.15 moles

2. Here we use Ar not Mr – it is atoms we’re being asked about
Ar of S = 32.1   Mass = Moles x Ar = 2.5 x 32.1 = 80.25g

3. Use Mr = mass ÷ moles = 8.4 / 0.3 = 28 so the molar mass is 28 g mol-1.
Suggests N2 or CO as possible identities.```

We use Avogadro’s number to work out actual numbers of atoms, ions or molecules (particles) in a given mass or number of moles of substance, or to work out the mass of a given number of particles.

In addition to the converting between mass and moles, we now need to use the equation:

number of particles = moles of particles × NA

or        moles of particles =    number of particles  ÷  NA

Application

How many atoms are there in 0.0005g of He ?

```convert mass to moles      moles = mass / Ar    = 0.0005 / 4
= 0.000125 mol

convert moles to atoms     atoms = moles x NA   = 0.000125 x 6.02x1023
= 7.525x1019 atoms              ```

What does a water molecule actually weigh?

```convert number to moles   moles = number / NA     = 1 / 6.02x1023
= 1.66x10-24

convert moles to mass      mass = moles x Ar      = 1.66x10-24 x 18
= 2.99x10-23 g```

### Moles of gases

It is more practical to work with volumes of gases rather than with masses. For this reason it is useful to know the molar gas volume (units: dm3 mol-1), which is the volume occupied by one mole of the gas. This will vary with temperature and pressure, but surprisingly does not vary from gas to gas (at least not for what we will consider ‘ideal gases’).

At room temperature and pressure (r.t.p: defined as 298K temperature and 100kPa pressure), one mole of any gas occupies a volume of 24 dm3 (which is 24,000 cm3) moles of gas   =   volume of gas  ÷  molar gas volume

volume of gas =   moles of gas  ×  molar gas volume

Remember to keep the volume of the gas and the molar gas volume in the same units – either dm3 or cm3!

The other useful property of gases is the density. This allows us to convert between mass and volume. Densities are typically measured in grams per cm3.

density  =  mass  ÷   volume            and                 mass = volume × density

Application

What is the volume of 0.10 moles of carbon dioxide at room temperature and pressure?

```volume = moles x molar gas volume         = 0.10 x 24
= 2.4 dm3   (or 2,400cm3)```

A gas is collected at room temperature and pressure, and found to have a density of 0.001333           g cm-3. Suggest the identity of the gas.

```mass of 1cm3 of gas = 0.001333g
mass of 24,000cm3 of gas = 0.001333 x 24,000 = 31.99g
therefore mass of 1 mole of gas (molar mass) = 31.99 g mol-1
Mr of gas = 31.99 (32 to two sig figs) so suggest gas might be O2```

### Historical Context

Our understanding of the structure of the atom has been refined as more sophisticated models have been proposed, and as experimental evidence has supported these models or caused them to be rejected.

Dalton’s model (early 1800s) was one of the first, proposing that atoms where solid spheres, and that each different element was made up of a different types of sphere.

Thomson’s experimental observations (1897) led to the conclusion that atoms could not be solid and indivisible. His results indicated that atoms contained much smaller negatively charged particles, which we now know to be electrons. The model of the atom was refined: a positively-charged sphere with negatively charged electrons embedded within it. This is sometimes referred to as the ‘plum pudding’ model.

Rutherford, with Geiger and Marsden (1909) experimented with firing positively charged alpha particles at an extremely thin gold sheet. They expected most of the alpha particles to be deflected slightly by repulsion from the positively charged ‘puddings’ in the foil. What they observed was that most alpha particles passed straight through, while a very small number were deflected backwards. A revised model was needed to explain these observations: the nuclear model, with a tiny positively charged nucleus at the centre of the atom, surrounded by a cloud of negatively charged electrons, and with most of the atom being empty space.

Mosely’s work on the charge of the nucleus of different atoms showed that nuclei of different atoms have different amounts of positive charge, the charge increasing from one element to another by units of one. Rutherford investigated further, discovering that the nucleus of an atom contains a number of positively-charged particles called protons, but Rutherford also realised that the nuclei of atoms were heavier than they should be if they contained only protons, and proposed that there must also be other particles with mass but no charge in the nucleus. These particles, neutrons, were eventually discovered by Chadwick supporting Rutherford’s model of the nucleus.

Bohr (1913) proposed a more sophisticated model of the ‘cloud’ of electrons, with the electrons arranged in fixed orbits (shells) each with a fixed energy. He suggested that electrons could move between the shells by absorbing or emitting an amount of energy equal to the difference between the energy levels of the shells. This would mean that the electrons in atoms would absorb or emit electromagnetic radiation (energy) with fixed frequencies. The fixed frequencies of radiation emitted and absorbed by atoms were already known from experiments – Bohr’s model allowed these observations to be explained.

Bohr’s model also stated that the shells could only hold fixed numbers of electrons, and that an element’s reactivity was related to the arrangement of these electrons. His model explained the observation that the noble gases (with their outer shell filled) were found to be stable and therefore unreactive (inert), while the alkali metals with one electron in their outer shell were found to be unstable and therefore reactive.

Bohr’s model is still used as it explains many phenomena such types of bonding between atoms, although even more sophisticated models based on quantum mechanics are available and are needed to explain observations such as the small variations in ionisation energies for atoms of successive elements across a period – we choose to use whichever model is most relevant to the observations we are trying to explain.

It is important to remember, though, that all models are simplifications, made to help us try to understand the complexity of the real world and to explain the experimental observations that we make, so that we can then make predictions and test them.