Electrons in Atoms Part 2 – Quantum Mechanical Model

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Electrons in Atoms Part 2 – Quantum Mechanical Model

Quantum Mechanical Model
As we saw earlier, the Bohr Model had several short comings The model currently used to describe the atom is the Quantum Mechanical Model of the atom This is the current theoretical framework that is used to describe all of the information we have about atoms and how they function

Basic Definitions Quantum (plural ‘quanta’) Mechanical
A finite amount of energy i.e. – an energy level in an atom The amount of energy required to move an electron from its present energy level to the next higher one Mechanical Movement of parts in relation to a whole i.e. – electrons in an atom Hence the Quantum Mechanical Model deals with the movement and location of electrons in an atom

Uncertainty Principle
The double-slit experiment showed that electrons could be anywhere, they are not confined to one path We cannot know where an electron is and where it is going Because of this, we use probability to determine where an electron is most likely to be

Electron Clouds Using the electron probabilities, we find areas where electrons are most likely to be These areas are called electron clouds where the probabilities of finding electrons is very high The shapes and distance from the nucleus of these electron clouds depends on several factors

Quantum Numbers To describe electron clouds and where electrons probably are, we use quantum numbers There are a total of four (4) quantum numbers as illustrated in the chart: Principal Quantum Number Angular Quantum Number Magnetic Quantum Number Spin Quantum Number

Quantum Numbers Principal Quantum Number n n can equal 1-7
Refers to the energy level or distance from the nucleus; Represented by the letter n. n is a number from 1-7 to describe the period on the periodic table the element is in Angular Quantum Number L L can equal 0 to (n-1) The shape of the orbital; represented the letters s, p, d, and f. Each letter also has a corresponding number s=0, p=1, d=2, f=3 Magnetic Quantum Number mL ml = -L to +L Determines the orientation of the orbital in space in reference to other orbitals Spin Quantum Number ms ms = +1/2 and -1/2 Specifies the value for spin; electrons in the same orbital must spin in opposite directions

Quantum Numbers Principal Quantum Number Energy level
Distance away from the nucleus As # increases, distance from the nucleus also increases As the number increases, so does the energy of the electrons in those orbitals Represented by integers 1,2,3,4,5,6,7 that correspond to the seven horizontal rows on the periodic table Determined by counting as you move down (top to bottom) the periodic table

Quantum Numbers Angular Quantum Number Also known as “sub-shells”
Refer to the shape of the orbital There are four (4) different shapes S, P, D, F These correspond to the s, p, d, f blocks on the periodic table

Quantum Number “S” Sub-shell Spherical shape N=0
Only one (1) orbital per energy level This is because the Magnetic Number, mL is from –L to +L The 1 sub shell can hold 2 electrons One with +1/2 spin One with -1/2 spin

Quantum Numbers “P” Sub-shell Dumbbell shape n=1
Three (3) orbitals per energy level mL and be from –L to +L Each shell can hold 2 electrons 3 orbitals mean the p-shell can hold up to 6 electrons

Quantum Numbers “D” Sub-shell Tend to have a clover- leaf shape n=2
Five (5) orbitals per energy level Each can hold a maximum of two (2) electrons Can hold a max of 10 electrons

Quantum Numbers “F” Sub-shell Shape contains 6 lobes for the most part
Seven (7) orbitals per energy level Each can hold a maximum of two (2) electrons Fourteen (14) electrons total at each energy level

To Summarize Sub-shell Energy level (n) in which it is first found
Number of sub-shells at a level Number of electrons in these sub-shells S 1 2 P 3 6 D 5 10 F 4 7 14

Quantum Numbers Spin Quantum Number
Remember, in each sub- shell there can be two (2) electrons These electrons must have spins that go in opposite directions Represented by arrows pointing in opposite directions

Quantum Number Example
Which of the following describes the 4p orbital? n=1, L=0 n=4, L=1 n=2, L=-1 n=3, L=0 Which of the following is not a possible set of quantum numbers? n=1, L=2, mL=-2 n=1, L=1, mL=-1 n=1, L=0, mL=1 n=1, L=0, mL= 0

Representing Electrons Using the Quantum Mechanical Model
There are two (2) different types of notation used to represent the quantum mechanical model: Orbital Notation Electron Configuration Notation

Orbital Notation Illustrates the following quantum numbers: principal, second (shape), and spin Use the template to draw and “fill” the sub- shells with electrons Order of filling electrons is governed by three (3) rules: Aufbau Principle Pauli Exclusion Principle Hund’s Rule

Orbital Notation Aufbau Principle: Pauli Exclusion Principle:
Electrons enter sub-shells of lowest energy first 1st energy level fills up before the next Pauli Exclusion Principle: All atomic sub-shells contain a maximum of two (2) electrons. Each MUST have a different spin Hund’s Rule: when electrons occupy sub-shells of equal energy, ONE electron enters EACH sub-shell until all the sub-shells contain one electron with identical directions Electrons are added to sub-shells so that a maximum number of unpaired electrons result

Examples Oxygen Titanium Strontium