The Structure of the Atom - Comprehensive Notes

The Atom

Overall Structure & Sub-atomic Particles

• The atom consists of three main subatomic particles:

  1. Electron
  2. Proton
  3. Neutron

• Important points:

  • Particles contribute to the atom's mass.
  • Electrons are located outside the nucleus, orbiting it.
  • Atoms of an element have the same number of protons and electrons (if not ions).
  • Neutrons reside in the nucleus and affect the atom's mass but have no charge.
  • The nucleus has a positive charge due to the presence of protons.

Important Measurements

1. The nucleus has a diameter of about 1 × 10^{-10} m.
2. The atom's diameter ranges from 1 × 10^{-10} m to 3 × 10^{-10} m.
3. Atomic radius is half the diameter.
   • Atomic radius increases down a group.
   • Atomic radius decreases across a period.
4. Ionic radius measures ion size.
   • Ionic radius increases with increasing negative charge.
   • Ionic radius decreases with increasing positive charge.

The Sub-atomic Particles

The Particles in an Electric Field

• Sub-atomic particles behave differently in an electric field due to their charge and mass:
  1. Electrons:
     • Negatively charged, attracted to the positive plate.
     • Easily deflected due to their light mass.
  2. Protons:
     • Positively charged, attracted to the negative plate.
     • Less easily deflected than electrons due to their heavier mass.
  3. Neutrons:
     • Not deflected due to having no charge.

Isotopes

• Isotopes are atoms of the same element with identical chemical properties but differing mass numbers.
• Isotopes of an element have the same number of protons and electrons but a different number of neutrons.

Relative Isotopic Mass

• The relative isotopic mass is calculated using the formula:
  Relative\ Isotopic\ mass\ of\ X = \frac{mass\ of\ an \ atom\ of\ isotope\ X}{\frac{1}{12}the\ mass\ of\ one\ atom\ of\ C^{12}}
• Similar to the Relative Atomic Mass (RAM) formula, but used specifically for isotopes.
• The key difference is that RAM uses the average mass of the element, whereas RIM uses the mass of a specific isotope.

Extending Atomic Symbols to Include Isotopes

• Atomic symbols are extended to include mass number and proton number.
• Example: Isotopes of Carbon (Carbon-12 & Carbon-14):
  • Carbon-12: 6 protons & 6 neutrons.
  • Carbon-14: 6 protons & 8 neutrons.

General Notation

• Notation:
  ^{mass\ number}_{proton\ number}Symbol

Ions

• Atoms form ions by losing or gaining electrons.
  1. Cations: Atoms that lose electron(s) and gain a positive charge.
  2. Anions: Atoms that gain electron(s) and gain a negative charge.

Notation

• Notation for an isotope which is an ion:
  ^{mass\ number}_{proton\ number}Symbol^{charge}

Calculating the Ar of Isotopic Mixtures

• Many elements occur naturally as a mixture of isotopes.

• The formula used for calculating the relative atomic mass is:
  Relative\ Atomic\ Mass = \frac{(Isotopic\ Mass × Relative\ Abundance) + (Isotopic\ Mass × Relative\ Abundance)}{100}

• Example: 3 isotopes of Carbon:

  1. Carbon-12: 98.89%
  2. Carbon-13: 1.108%
  3. Carbon-14: 1×10^{-10}

• Find the Relative Atomic Mass of the three isotopes:

RAM = \frac{(12 × 98.89) + (13 × 1.108) + (14 × (1 × 10^{-10}))}{100}

RAM = \frac{1186.68 + 14.404 + (1.4 × 10^{-9})}{100}

RAM = \frac{1201.084 \ amu}{100}

\approx 12.011 \ amu

A_r = 12.011

Chemical Energy

• Chemical energy consists of two components:
  1. Kinetic Energy: Measure of the motion of atoms.
  2. Potential Energy: Measure of how strongly the particles attract one another.

Kinetic Energy

• Kinetic energy increases as the temperature increases.
• Chemists use the absolute temperature scale, where kinetic energy is directly proportional to temperature.
• Three main types of kinetic energy:
  • Translation: Movement from place to place. For monoatomic gases, all kinetic energy is translational.
  • Rotation: Diatomic gas molecules rotate about the center of the bond.
  • Vibration: Diatomic gas molecules vibrate as if joined by a spring.

Kinetic Motion in Each State

Potential Energy

• Potential energy is usually greater than kinetic energy at normal temperatures.
• It provides information about the strengths of chemical bonds.

Causes

• Potential energy arises from attractions and repulsions between atoms, ions, and molecules.
• These interactions follow the basic principles of electrostatics:
  • Like charges repel.
  • Opposite charges attract.

Explanation

• Consider Na^+ and Cl^-, which are attracted to each other.
• Energy is required to separate them, increasing the potential energy of the system as force F is applied over a distance d.
• Bringing separated Sodium and Chlorine atoms together decreases potential energy.

Arrangement of Electrons: Energy Levels & Orbitals

Energy Levels in the Atom

• Hydrogen, a small spherical atom with a proton and electron, has electrostatic attraction between the two particles.
• Energy levels stem from different electrostatic potential energy states corresponding to varying distances of the electron from the nucleus.
• These energy levels are called orbitals and are arranged in shells containing similar energies.
• The number of orbitals in a shell is determined by the formula:

no.\ of\ orbitals\ in\ shell\ n = n^2

• where n is the principal quantum number.

Sub-shells & Orbital Shapes

The First Shell: S Orbital

• The single orbital in the first shell is spherically symmetrical.
• The probability of finding the electron at a given distance from the nucleus is the same in all directions.
• This orbital is known as the 1s orbital.

The Second Shell: S and P Orbitals

• This shell contains 4 orbitals:
  • One spherically symmetrical 2s orbital.
  • Three p orbitals with an odd 8 shape aligned along the three different axes (3px, 3py, 3pz).

The Third Shell: S, P, & D Orbitals

• This shell has 9 orbitals in total:
  1. One spherically symmetrical 3s orbital.
  2. Three 3p orbitals with two lobes pointing along the axes (3px, 3py, and 3pz).
  3. Four d orbitals with 4 lobes on the same plane at right angles (3dxy, 3dxz, 3dyz, and 3dx^2-y^2).
  4. One two-lobed orbital with a donut shape (3dz^2).

The Fourth Shell: S, P, D, & F Orbitals

• This shell contains 16 orbitals: one 4s orbital, three 4p orbitals, five 4d orbitals, and seven 4f orbitals.
• Each of the 4f orbitals has multiple lobes pointing away from each other.

Shells & Orbitals in Summary

Putting Electrons into Orbitals

• The most stable electronic configuration of an atom has the lowest amount of energy.
• The order in which sub-shells are filled depends on their relative energy.
• The filling order is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, and so on.

Ground State

• Filling orbitals with the lowest energy levels results in a stable electronic configuration, known as the ground state.

Electron Configuration

• In IGCSE chemistry, electronic configuration was written as: e.g., Potassium: 2, 8, 8, 1
• In AS level, this format is expanded to include the principal quantum number and sub-shell.
• Two methods:
  1. Full Electronic Configuration
  2. Shorthand Electronic Configuration
  3. Box Electronic Configuration

Full Electronic Configuration

• Example with potassium (19 electrons):

• 4s shell has a lower energy level than the 3d shell, therefore it fills first.
• The full configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1.

Shorthand Electronic Configuration

• Uses the closest previous noble gas to represent complete shells.
• Potassium example:
  1. Closest noble gas to potassium is Argon (Ar), which has the electronic configuration 1s^2 2s^2 2p^6 3s^2 3p^6.
  2. Potassium has one more electron than Argon, so add 4s^1.
  • Shorthand: [Ar] 4s^1

Box Electronic Configuration

• A visual representation of electronic configuration.

The Basics

• Uses boxes to represent orbitals; each box holds a maximum of 2 electrons.

• Rules:
  1. Each box can contain a maximum of 2 electrons.
  2. Fill each orbital with one electron first, then add the second electron.
  • Example: filling the p orbital with 4 electrons:
    • Empty boxes: _ _ _
    • Fill each box with one electron (spin up): ↑ ↑ ↑
    • Fill from box one again with a downward pointing arrow (spin down): ↑↓ ↑ ↑

Example

• Rubidium (37 electrons):
  • Shell 1: 1s^2
  • Shell 2: 2s^2 2p^6
  • Shell 3: 3s^2 3p^6 3d^{10}
  • Shell 4: 4s^2 4p^6
  • Shell 5: 5s^1

Steps

1. Create the table:

2. Start filling the boxes with arrows representing electrons, following the rules:

3. Re-arrange all of the boxes and put them beside each other from lowest to highest energy level
   ```
   1s 2s 2p 3s 3p 4s 3d 4p 5s
   ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑

4. Now, this isn’t the correct way to write it which is why we shall put it in the correct format now.
   Basically, we take all of the boxes and put them beside each other from lowest to highest energy level.
   1s 2s 2p 3s 3p 4s 3d 4p 5s
   ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑

Spin-pair Repulsion

• Electrons in the same region of space repel each other due to their like charges; this is spin-pair repulsion.
• Electrons first occupy separate sub-shells to minimize repulsion, spinning in the same direction.
• When no empty orbitals are left, electrons pair up in orbitals, spinning in opposite directions to minimize repulsion.

Free Radicals

• A free radical is a species with one or more unpaired electrons.
• Rubidium example: the radical electron is in the 5s orbital, which contains one unpaired electron.

Electronic Configuration of Ions

• Two types of ions:

Positive Ions

• Formed when electrons are removed from atoms.
• Potassium ion example: a Potassium ion has 18 electrons, while a neutral Potassium atom has 19 electrons, configuration: 1s^2 2s^2 2p^6 3s^2 3p^6.

Negative Ions

• Formed when electrons are gained by atoms.
• Chlorine ion example: A Chlorine ion has 18 electrons, while a neutral Chlorine atom has 17 electrons, configuration: 1s^2 2s^2 2p^6 3s^2 3p^6.

Ionisation Energy

• Ionisation energy (IE) is defined as the energy required to remove one mole of electrons from one mole of gaseous atoms (or ions).
• Key points:
  1. General symbol for ionisation energy is IE.
  2. The unit for IE is kJ mol-1.
  3. IE is measured under standard conditions (298 K and 101 kPa).

Making Equations for Ionisation Energies

First Ionisation Energy

• Remove one electron from an atom:

K(g) → K^+(g) + e^−

Second Ionisation Energy

• Remove one electron from a positive ion:

K^+(g) → K^{2+}(g) + e^−
*Ionisation energy is measured with the substance in its gaseous state.

Successive IEs

• Electrons can be successively removed from an atom.
• When writing equations, remember:
  1. Atoms and ions are in a gaseous state.
  2. The charge on the ion on the right-hand side gives the number of the IE.

Trends in IEs

Factors Affecting IE

• Four main factors affect the first IE:
  1. Size of nuclear charge.
  2. Distance of the outermost electron(s) from the nucleus.
  3. Shielding effect of inner electrons.
  4. Spin-pair repulsion.

What is Shielding?

• Electrons repel each other due to their negative charge.
• Inner shell electrons repel outer shell electrons, reducing the effective nuclear charge felt by the outer electrons.
• The number of shells increases the shielding effect.

Trend of IE across the Period

• IE generally increases across a period due to:
  • Increasing nuclear charge.
  • Decreasing distance between outermost electron(s) and the nucleus.
  • Shielding effect remains relatively constant.
  • Spin-pair repulsion depends on the element.

Why the IE Drops Sometimes

• Two main reasons for IE drops:

  1. Complete shells
  2. Spin-pair repulsion

• Complete Shells

  • Occurs between Boron (B) and Beryllium (Be).
    1. B: 1s^2 2s^2 2p^1
    2. Be: 1s^2 2s^2
  • Beryllium has a complete orbital, which results in a high IE. Boron has a lower IE as it does not have a complete orbital as compared to Beryllium

• Spin-pair Repulsion

  • Occurs between Nitrogen (N) and Oxygen (O).
    1. N: 1s^2 2s^2 2p^3
    2. O: 1s^2 2s^2 2p^4
  • Oxygen has no unpaired electrons and the spin-pair repulsion makes it easier to remove the electron.
  • Nitrogen has an unpaired electron without any spin-pair repulsion.
    *When the scenario is similar to the ones with Boron & Beryllium or Nitrogen & Oxygen. we give the same answer as the period 1 elements (depending on the scenario) as the pattern doesn’t really change.

Trend from Period to Period

• IE decreases from one period to the next due to:
  • The addition of shells, increasing the distance of electrons from the nucleus.
  • Increased shielding.

Trend of IE Down the Group

• IE decreases down the group due to:
  • Increasing nuclear charge.
  • Number of shells increases therefore the distance between the outer electron and nucleus increases.
  • Increased shielding.

Finding Electronic Configuration Using IE

Steps

1. Find where the biggest jump in IE takes place.
2. Choose the smaller IE number before the jump.
3. Locate the element with the corresponding group number and period.
4. Write down the electronic configuration.

Example Question: Sulfur

• Element X is in period 3.

Solution

1. The largest IE jump occurs from the 6th to the 7th IE.
2. Select the number of the IE that is a lesser value, which is 6.
3. Sulfur is located in group 6 of period 3.
4. Sulfur (16 electrons): 1s^2 2s^2 2p^6 3s^2 3p^4.

Explanation

• The large IE jump between the 6th and 7th electrons indicates that the 7th electron is in a different shell closer to the nucleus.
• This suggests that the element is in group 6.

Atomic Radius & Ionic Radius

Atomic Radius

• Atomic radius is the distance from the nucleus to the outermost orbital of its electron.

Trend down the Group

• Atomic radius increases down the group due to:
  • The number of shells increases which also increases the shielding.
  • Inner shell electrons repel outermost electrons, shielding them from nuclear charge.

Trend across the Period

• Atomic radius decreases across the period due to:
  • The number of protons increases which leads to force of attraction increasing.
  • Inner shell electrons repel outermost electrons, shielding them from nuclear charge.

Ionic Radius

Trend down the Group

• Ionic radius increases down the group:
  • The number of shells increases and, as such, the distance between outermost shell and nucleus increases
  • Increased shielding outweighs the higher nuclear charge.
  • The number of electrons lost or gained by elements in the group is similar.

Trend across the Period

• Ionic radius decreases across the period due to:
  1. Increasing nuclear charge and constant number of shells attracts outer shell electrons closer to the nucleus.
  2. Cations are typically smaller than anions because they lose their outermost shells, while anions do not.