Week 4 Lecture 2 - Topic 4 (Atomic energy levels)

Stoichiometry Review

Stoichiometry is crucial in chemistry, dealing with the ratios in which substances react and the amounts of products formed.
It involves understanding the ratio of reactants to each other (e.g., 1:1, 1:2, 3:5) and to the products they create.
This is all based on the mole concept, where one mole equals Avogadro's number of particles (6.022 \times 10^{23}).
To understand these ratios, balanced equations are essential.
With a balanced equation, mole ratios can be used to determine the amount of a product or the required amount of a reagent.
Concepts like limiting reagents (the reagent that limits the amount of product formed) are important.
Percentage yields can be calculated by relating the actual yield to the theoretical yield.
Solution stoichiometry applies these principles to reactions in solution, considering how salts behave.
For example, sodium chloride (NaCl) solvates into sodium cations (Na+) and chloride anions (Cl-).
Polyatomic salts like phosphate (Na2PO4) produce multiple moles of ions upon dissolving.
Spectator ions do not participate in the reaction and remain unchanged on both sides of the equation.

Atomic structure and makeup are related to chemical reactivity.
Understanding atomic energy levels creates a foundation for understanding the nature of elements and compounds.
An atom consists of a nucleus containing neutrons (neutral charge) and protons (positive charge).
The nucleus gives an atom its mass, determined by the number of neutrons and protons.
Electrons surround the nucleus in a cloud, occupying different energy levels.
The positive charge of the nucleus is balanced by the negative charge of the electrons, making the atom electrically neutral.
Ions are formed when an atom gains or loses electrons, thus upsetting the balance.

Light exhibits both wave-like and particle-like properties.
As a wave, light has oscillations with peaks and troughs, characterized by frequency and wavelength.
Wavelength is the distance from one peak to the next, and frequency is the number of waves passing a point per second.
There is an inverse relationship between wavelength and frequency: longer wavelength means lower frequency, and vice versa.
Amplitude is the intensity of the wave.
Light exists on a spectrum from long radio waves to short gamma rays.
Visible light is a small portion of this spectrum, which can be broken up into its component colors using a prism.
Different colors correspond to different energies.
Gamma rays have high energy, while radio waves have relatively low energy.
The photoelectric effect demonstrates that the energy of light depends on frequency and intensity.
Einstein proposed that light energy comes in packets called photons.

Each photon has energy that can be described by the formula: E = h \times v, where:
- E is the energy of the photon
- h is Planck's constant (6.62 \times 10^{-34} \text{ joules} \cdot \text{ second}) (provided on exam data sheet)
- v is the frequency.
The energy of a photon relates to the binding energy of an electron.
Light is absorbed by and reflected off of objects, giving them color based on the wavelengths absorbed and reflected.
When an electron absorbs energy, it can become excited and jump to a higher energy level.
Ground state is the electron's lowest energy state, while an excited state is higher energy and unstable.
When an electron returns to its ground state, it emits a photon with energy equal to the energy difference between the levels.
Atoms interact with light differently.
Each atom has a unique atomic spectrum.
When they absorb light (photons), electrons are raised to higher energy levels and then relax back to their ground state.
Emission spectra show the light given off when electrons relax, appearing as different colors.

Each element has a distinctive emission spectrum with specific wavelengths.
For example, hydrogen has four distinct emission lines, indicating four different energy levels.
Sodium lamps emit yellow light due to their emission spectra.
Flame tests demonstrate this by showing different colors when metal salts are heated, based on the energy levels of their atoms.
The energy levels of electrons are quantized, meaning they are discrete amounts.
It takes a certain amount of energy to get between energy levels. If the amount of energy applied is insufficient, the jump between energy levels will not happen.
The amount of energy released when an electron returns to its ground state is exactly the same as the amount of energy it absorbed to reach the excited state.
The change in energy of the atom equals the change in the energy of its electrons, which equals the energy of the emitted photon.
Electrons may relax back to their ground state in multiple stages, emitting different photons (colors) at each stage.
For example:
- An atom absorbs energy and its valence electrons go to energy level two from the ground state.
- Another atoms absorbs more energy therefore its valence electrons go to energy level six from the ground state.
- The atom releases the electron back to other other levels, so it releases photons of different energy, giving it a particular color.

All electrons have the same mass, which is so small that it negligibly contributes to the mass of the atom.
They have a magnetic property called spin.
The uncertainty principle states that it is impossible to know with certainty both the position and momentum of an electron at the same time.
We can only describe the probability of finding an electron in a certain location; electrons are spread out rather than located in a particular spot.
Schrödinger's equation describes how electrons are distributed, leading to the concept of orbitals.
Orbitals describe the probability of where an electron can be found and provide information about its energy.
Quantum numbers are used to describe electrons, providing information about their energy and location.
Quantum numbers are like coordinates on a map for locating electrons, reflecting their energy, and if they will be involved in reactions or not

Principal quantum number (n) defines the energy level and shell of an electron. Principal quantum number is the most relevant quantum number because other quantum number depend to it.
The nucleus has the first orbital around it. Each orbital have different labels. The principal quanutm number of the innermost orbital is n = 1, which indicates the lowest energy level with maximum 2 electrons.
For the next energy levels, the principal quantum numbers are: n = 2, max, eight electrons in this shell or orbital; n = 3, max, of eight electrons.
Each period of the periodic table corresponds to a shell, which have different principal quantum numbers.
Therefore n = 1 correlates to the 1st row of the periodic table.
The amount of electrons in a valence in the outermost orbital corresponds to the element location at the periodic table
For example: Sodium; It has an atomic # of 11
- We see that that matches up with our idea of these shells.
- We have two in this innermost shell\, two electrons there because that's full because we've gone from here to here.
- That one is full, so we've got to jump up to the next shell which has a higher energy level.
- And one electron in n=3 in that outermost shell\, and we have a total of 11 electrons altogether.