Module 3 Lesson 2: Electron Cloud Model and Electron Orbitals

Introduction to the Electron Cloud Model

• The electron cloud model is also widely known as the quantum mechanical model of the atom.

• The pioneer and primary developer of this model is Erwin Schrödinger.

• Schrödinger developed the fundamental mathematical equations used to explain and predict electron behavior.

• A significant limitation of the previous Bohr model was its simplified view of electron motion. In the electron cloud model, electrons do not travel around the atom's nucleus in predetermined, neat, circular orbits.

• The exact location and specific path of an electron at any given time cannot be known with certainty.

• Electrons exist in "clouds of probability" around the nucleus. Probability in this context means that while there is a high likelihood an electron is in a specific region, its presence is not guaranteed at a specific point.

• The electron cloud is defined as the area surrounding the nucleus where there is a high probability of finding an electron.

• Visual interpretation of the model:

  • Darker regions within the cloud represent areas of higher probability for finding an electron.

  • Light regions represent lower probability.

  • Energy levels are still present and appear as distinct darker bands within the cloud.

• The electron cloud model is the currently accepted scientific model of the atom.

Electron Orbitals and Energy Levels

• An orbital is a specific three-dimensional region around the nucleus that describes where an electron is likely to be found.

• The electron cloud is composed of these various orbitals.

• Relationship to energy:

  • Bohr's observation that electrons exist in energy levels remains correct.

  • Electrons possess higher or lower energy based on their specific location and distance from the nucleus.

  • As an orbital's distance from the nucleus increases, the energy level associated with that orbital increases.

• Orbital Shapes:

  • Unlike the flat rings of the Bohr model, orbitals have distinct three-dimensional shapes.

  • An atom can contain one or many orbitals, determined solely by the number of electrons it possesses.

  • Each individual orbital has a maximum occupancy of $2$ electrons.

The Quantum Number System (Coordinate Address)

• Because electron location is complex, scientists use a system of numbers to describe the probable location of an electron.

• This system functions like a coordinate system or a mailing address for an electron.

• Analogy for levels of organization:

  • Energy Level = The city (e.g., Charlotte, North Carolina).

  • Sublevel = Specific streets within the city.

  • Orbital = The house numbers on تلك streets.

The Principal Quantum Number

• Abbreviated with the lowercase letter $n$.

• It identifies the main energy level of the orbital and the overall size of the orbital.

• Properties of $n$:

  • As the value of $n$ increases, the size of the orbital increases.

  • As the value of $n$ increases, the energy value of the orbital increases.

  • Higher $n$ values indicate that the electron is, on average, further away from the nucleus.

• Alternative names for this value include the "electron shell" or the "main level."

• Atomic Stability: Atoms are considered most stable when they are at their lowest energy state. This occurs when electrons occupy the lowest energy shells available.

Angular Momentum Quantum Number

• Abbreviated with the lowercase letter $l$.

• This number represents the specific shape of the orbital, also known as the subshell or sublevel.

• The shapes are categorized by the letters $s$, $p$, $d$, and $f$:

  • $s$ orbital: Spherical shape.

  • $p$ orbital: Shaped like a dumbbell or an infinity symbol.

  • $d$ orbital: Typically shaped like a cloverleaf.

  • $f$ orbital: Extremely complex shapes with many features.

• Note: While visual models show distinct edges for these shapes, in reality, electrons exist in clouds with no clearly defined boundaries.

Magnetic Quantum Number

• Abbreviated with the lowercase letter $m$.

• This number represents the orientation of the orbital along the $x$, $y$, and $z$ axes.

• Orientation and Orbital Counts:

  • $s$ sublevel: Only $1$ orientation exists because a sphere looks the same from every angle. Therefore, identifying an $s$ sublevel means there is only $1$ orbital.

  • $p$ sublevel: Has $3$ distinct orientations (lining up along the $x$, $y$, and $z$ axes). This sublevel consists of $3$ separate orbitals.

  • $d$ sublevel: Has $5$ different orientations/orbital shapes.

  • $f$ sublevel: Has $7$ different orientations due to its high complexity.

• Memory Aid: The number of orbitals in the subshells $s, p, d, f$ follows a sequence of odd numbers: $1, 3, 5, 7$.

The Apartment Building Analogy

• Purpose: To clarify the hierarchical relationship between energy levels ($n$), sublevels ($s, p, d, f$), orbitals (rooms), and electrons (occupants).

• Building Components:

  • Floors of the building = Main energy levels ($n = 1, 2, 3, 4$).

  • Apartment types = Sublevels ($s, p, d, f$).

  • Rooms in the apartment = Orbitals.

  • Maximum occupancy = $2$ electrons per room (orbital).

Distribution by Energy Level

• Energy Level $1$ ($n = 1$):

  • Contains only $1$ sublevel: the $s$ apartment.

  • The $s$ apartment has only $1$ room (orbital).

  • Total Orbitals: $1$.

  • Maximum Electrons: $2$.

• Energy Level $2$ ($n = 2$):

  • Contains $2$ sublevels: the $s$ and $p$ apartments.

  • $s$ has $1$ room; $p$ has $3$ rooms.

  • Total Orbitals: $1 + 3 = 4$.

  • Maximum Electrons: $4 \times 2 = 8$.

• Energy Level $3$ ($n = 3$):

  • Contains $3$ sublevels: $s$, $p$, and $d$ apartments.

  • $s$ has $1$ room; $p$ has $3$ rooms; $d$ has $5$ rooms.

  • Total Orbitals: $1 + 3 + 5 = 9$.

  • Maximum Electrons: $9 \times 2 = 18$.

• Energy Level $4$ ($n = 4$):

  • Contains $4$ sublevels: $s$, $p$, $d$, and $f$ apartments.

  • $s$ has $1$ room; $p$ has $3$ rooms; $d$ has $5$ rooms; $f$ has $7$ rooms.

  • Total Orbitals: $1 + 3 + 5 + 7 = 16$.

  • Maximum Electrons: $16 \times 2 = 32$.

Global Pattern of Sublevels

• The number of sublevels typically correlates with the principle energy level number up to a point:

  • $n = 1$: $1$ sublevel ($s$)

  • $n = 2$: $2$ sublevels ($s, p$)

  • $n = 3$: $3$ sublevels ($s, p, d$)

  • $n = 4$: $4$ sublevels ($s, p, d, f$)

• Beyond the fourth level, the pattern reverses:

  • $n = 5$: $4$ sublevels ($s, p, d, f$)

  • $n = 6$: $3$ sublevels ($s, p, d$)

  • $n = 7$: $2$ sublevels ($s, p$)

Questions & Discussion

Question 1: How many sublevels are there in the $n = 3$ shell/energy level?

• Step 1: Identify the energy level: $n = 3$.

• Step 2: Recall the sublevel rule: the number of sublevels corresponds to the level number for levels 1-4.

• Step 3: List the sublevels: $s, p, d$.

• Answer: There are $3$ sublevels.

Question 2: How many orbitals are there in the $n = 5$ energy level?

• Step 1: Identify the energy level: $n = 5$.

• Step 2: Recall the pattern. After level 4, the counts begin to decrease/repeat level 4’s structure. Level 5 has $4$ sublevels.

• Step 3: Identify the sublevels: $s, p, d, f$.

• Step 4: Count the orbitals for each: $s(1) + p(3) + d(5) + f(7)$.

• Step 5: Calculate the total: $1 + 3 + 5 + 7 = 16$.

• Answer: There are $16$ orbitals.

Question 3: What is the maximum number of electrons that can occupy the $n = 2$ energy level?

• Step 1: Identify common energy level: $n = 2$.

• Step 2: Determine sublevels for level 2: $s$ and $p$.

• Step 3: Calculate total orbitals: $s$ has $1$ orbital; $p$ has $3$ orbitals ($4$ total orbitals).

• Step 4: Multiply orbitals by the occupancy limit ($2$ electrons per orbital).

• Step 5: Calculation: $4 \times 2 = 8$.

• Answer: The maximum number is $8$ electrons.