WednesdayOctober 24, 2012(Main and Sub-Energy Levels, Orbitals; Aufbau, Hund, and Pauli; Quantum Numbers;

WS – Arrangement of Electrons in Atoms)

Bell RingerWednesday, 10-24-12

Write the•isotopic notation

•electron configuration

notation•Lewis Dot Structure

for the following atoms:

Be, B, N, F, Mg, Al, Ca, Br

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Main Energy LevelsAn atom can have up to 7 main energy

levels, which we have called

“lanes of the track.” These correspond to

the 7 periods of the Periodic

Table.

The main energy levels can further divided into sublevels, which we call s, p, d, and f.

Energy level 1 – s-sublevel onlyEnergy level 2 – s- and p-sublevels

Energy level 3 – s-, p-, and d-sublevelsEnergy level 4 – s-, p-, d-, and f-sublevelsEnergy level 5 – s-, p-, d-, and f-sublevels

Energy level 6 – s-, p-, and d-sublevelsEnergy level 7 – s-sublevel only (so far)

Remember that s-sublevels can hold up to 2 electrons, p-sublevels up to 6 electrons, d-sublevels up to 10 electrons, and f-sublevels up to 14

electrons.

Energy Sub-Levels

An orbital is like a shoebox with electrons being the shoes.An electron “orbital” can hold only 2 electrons, regardless of the energy sublevel

it is in.

Since an s-sublevel can only hold 2 electrons, it can contain only 1 orbital.

A p-sublevel can hold 6 electrons, so it can contain 3 orbitals.

A d-sublevel can hold 10 electrons, so it can contain 5 orbitals.

An f-sublevel can hold 14 electrons, so it can contain 7 orbitals.

Orbitals

These three laws must be followed by electrons in orbitals of an atomic cloud.

The Aufbau Principle

Hund’s Rule

The Pauli Exclusion Principle

Rules for Electron Insertion into the Electron Cloud

The Aufbau

PrincipleAn electron occupies the

lowest energy

orbital that can receive

it

ExampleThe 4s

orbital is filled before

the 3d

Hund’s Rule

Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a

second electron, and all electrons

in singly occupied orbitals must

have the same spin.

_____ _____ _____2px 2py 2pz

Hund’s Rule

Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a

second electron, and all electrons

in singly occupied orbitals must

have the same spin.

All students will try to get their own seat

on a separate row until all rows are

filled with one student. Only then will they begin to

double-up.

A school bus after a rainstorm

The Pauli Exclusion Principle

No two electrons in the same atom can have the same set of four quantum numbers.

Electrons occur in pairs with opposite spins.

The Principle Quantum NumberThe principal quantum number (n) indicates the main energy level occupied by the electron.

Values of n are positive integers only - 1, 2, 3, and so on.

As n increases, the electron’s energy and its average distance from the nucleus increase.

For example, an electron for which n = 1 occupies the first, or lowest, main energy level

and is located closest to the nucleus.

As you will see, more than one electron can have the same n value, and these electrons are sometimes said to be in the same electron shell.

The total number of orbitals that exist in a given shell, or main energy level, is equal to n2.

The Angular Momentum Quantum Number

The angular momentum quantum number, (l), indicates the shape of the orbital. Except at the

first main energy level, orbitals of different shapes (known as sublevels) exist for a given

value of n. For a specific main energy level, the number of orbital shapes possible is equal to n. The values of l allowed are zero and all positive

integers less than or equal to n − 1. For example, orbitals for which n = 2 can have one of two shapes corresponding to l = 0 and l = 1

The Angular Momentum Quantum NumberDepending on its value of l, an

orbital is assigned a letter. s orbitals are spherical, p orbitals

have dumbbell shapes, and d orbitals are more complex. (The f orbital shapes are too complex to discuss here.) In the first energy

level, n = 1, there is only one sublevel possible - an s orbital. As

mentioned, the second energy level, n = 2, has two sublevels - the s and p orbitals. The third energy level, n = 3, has three sublevels -

the s, p, and d orbitals. The fourth energy level, n = 4, has four

sublevels - the s, p, d, and f orbitals. In an nth main energy level, there

are n sublevels

The Angular Momentum Quantum NumberEach atomic orbital is designated by the principal quantum number

followed by the letter of the sublevel. For example, the 1s sublevel is the s orbital in the first main energy level, while the 2p sublevel is the set of p orbitals in the second main energy level. On the other hand, a 4d orbital is part of the d sublevel in the fourth main energy level. How would you designate the p sublevel in the third main energy level? How many other sublevels are in the same main energy level with this one?

The Magnetic Quantum NumberThe magnetic quantum number, (m), indicates the orientation of an orbital

around the nucleus. Atomic orbitals can have the same shape but different

orientations around the nucleus. Here we describe the orbital orientations that

correspond to various values of m. Because an s orbital is spherical and is

centered around the nucleus, it has only one possible orientation. This

orientation corresponds to a magnetic quantum number of m = 0. There is therefore only one s orbital in each s

sublevel.

s-orbitals: m = 0

The Magnetic Quantum NumberThe lobes of a p orbital can extend along the x, y, or z axis of a

three-dimensional coordinate system. There are therefore three p orbitals in each p sublevel, which are designated as

px, py , and pz orbitals. The three p orbitals occupy different regions of space and correspond, in no particular order, to

values of m = −1, m = 0, and m = +1 so far.p-orbitals: m = -1, m = 0, m = +1

There are five different d orbitals in each d sublevel.

The five different orientations, including one with a different

shape, correspond to values of m = −2, m = −1, m = 0, m = +1,

and m = +2

The Magnetic Quantum Number

There are seven different f orbitals in each f sublevel. The total number of orbitals at a main energy level increases with the value of n. In fact, the number of orbitals at each main energy level equals the square of

the principal quantum number, n2. What is the total number of orbitals in the third energy level? Specify each of the sublevels using the three

quantum numbers you’ve learned so far.

The Magnetic Quantum Number

Like Earth, an electron in an orbital can be thought of as spinning on an internal axis. It spins in one of two possible directions, or states. As it spins, it creates a

magnetic field. To account for the magnetic properties of the electron, theoreticians of the early

twentieth century created the spin quantum number. The spin quantum number has only two possible

values (+1/2 , −1/2) which indicate the two fundamental spin states of an electron in an orbital. A

single orbital can hold a maximum of two electrons, which must have opposite spins.

The Spin Quantum Number

Arrangement of Electrons in Atoms

Worksheet