week 1 quantum theory&atomic orbitals

Prepared by:Mrs Faraziehan Senusi

PA-A11-7C

Quantum Theory

Atomic Orbitals

Electronic Configuration

Chapter 1Atoms, Molecules & Chemical bonding

Molecular Orbitals

Bonding and Intermolecular Compounds

David P. White Prentice Hall ©

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Introduction


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Hydrogenic Orbitals

Wave functions

Shells and subshells

Atomic Orbitals

Quantum Theory

Lesson Plan


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At the end of this topic, the students will be able:

To describe atomic orbitals. To write electronic configurations To explain the bonding between different atoms To explain the interactions between molecules

• Schrödinger proposed an equation that contains both wave and particle terms.

• The important point is that each solution of the Schrödinger wave equation () describes a possible energy state for the electrons in a hydrogen atom.

• Each solution is described by a set of quantum numbers.

• Solutions of the Schrödinger equation also tell us about the shapes and orientations of the probability distributions of the electrons.


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Quantum Mechanics and Atomic Orbitals

• The square of the wave function, gives the probability of finding the electron, that is, gives the electron density for the atom.

• Each solution to the equation (that is, each energy state of the atom) is associated with a given wave function, also called an atomic orbital.

• Atomic orbital can be thought as the wave function of an electron in an atom.

• An orbit is an electron’s path around the nucleus whereas, an orbital is a mathematical function with no direct physical meaning.


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An atomic orbital is specified by 3 quantum numbers:1. Principal Quantum Number, n, related to the size of the orbital.

This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. The higher the value of n, the higher the energy level.

2. Orbital Angular Momentum (or, Azimuthal) Quantum Number, l. (related to shape of orbital). This quantum number depends on the value of n. The number of l value = the number of n value. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3, respectively). Usually we refer to the s, p, d and f-orbitals.

3. Magnetic Quantum Number, ml related to orientation in space. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. The number of possible ml values equals the number of orbitals, which is 2l+1 for a given l value.

to describe the distribution of electrons in hydrogen and other atoms.


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Summarizes the hierarchy among the three quantum numbers:


Determining l values for n = 3, l = 0,1,2Determining ml for each l value:

• For l = 0, ml = 0

• For l = 1, ml = -1, 0, +1

• For l = 2, ml = -2,-1,0,+1,+2

There are nine ml values, so there are nine orbitals with n = 3.

The total number of orbitals for a given n value is n2,

and for n = 3, n2 = 9.David P. White

Prentice Hall © 2003

ExampleWhat values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals exist for n = 3?


The energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers:

Shell/Level - The atom's energy levels, or shells, are given by the n value: the smaller the n value, the lower the energy level and the greater the probability of the electron being closer to the nucleus.


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Subshell/Sublevel - The atom's levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation:

l = 0 is an s subshell l = 1 is a p subshell

l = 2 is a d subshell l = 3 is an f subshell

The letters derived from the names of spectroscopic lines: sharp, principal, diffuse and fundamental

Subshells are named by joining the n value and the letter designation. For example, n=2 and l=0 is called 2s subshell.


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Orbital – Each allowed combination of n, l and ml values specifies one of the atom’s orbitals to describe the shape, size and the spatial orientation. The value of n = the number of possible l values (an

integer from 0 to n-1). So, when n = 2, l will have only two values, 0 and 1.

The number of orbitals in each subshell is 2l+1 for a given l value.

One s orbital (l=0), 3p orbitals (l=1) and 5d orbitals (l=2) and 7f orbitals (l=3).

• Each sublevel of the H atom consists of a set of orbitals with characteristic shapes.

The s Orbital• An orbital with l = 0 has a spherical shape with the nucleus at

its center and is called an s orbital.• The H atom's ground state, for example, has the electron in the

1s orbital, and the electron probability density is highest at the nucleus.

• An s orbital has a spherical shape, so it can have only one orientation and, thus, only one value for the magnetic quantum number: for any s orbital, ml = 0.


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Shapes of Atomic Orbitals


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The s-Orbitals


The p Orbital• An orbital with l = 1, called a p orbital, has two

regions of high probability, one on either side of the nucleus.

• The orbitals are dumbbell shaped.• There are three p-orbitals px, py, and pz.

• The three p-orbitals lie along the x-, y- and z- axes.• The letters correspond to allowed values of ml of -1,

0, and +1.


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The p - Orbitals



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The d Orbital• An orbital with l = 2 is called a d orbital.

• There are five possible ml values for the l = 2 value: -2, -1, 0, + 1, and +2.

Orbitals with Higher l Values• There are seven f orbitals (2l+1=7), each with a

complex, multilobed shape.

• Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation.


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Example• The 2s sublevel has only one orbital, and its

quantum numbers are n = 2, l = 0, and ml = 0.

• The 3p sublevel has three orbitals: n = 3, l = 1, and ml = -1;

n = 3, l = 1, and ml = 0;

n = 3, l = 1, and ml = +1.


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Example

How many orbitals exist for n = 3?For n = 3, l will have 3 values, i.e., 0, 1 and 2.

For l = 0, ml will have 0 value (0)

For l = 1, ml will have 3 values (-1, 0 and +1)

For l = 2, ml will have 5 values, -2 through 0 to +2. (-2, -1, 0 ,+1 and +2).

There are 9 ml values which means 9 orbitals.

In other words, n2=32=9.

• A fourth quantum number – the spin quantum number.• The spin quantum number, ms, refers to the spin of an

electron and the orientation of the magnetic field produced by this spin.

• For every set of n, l, and ml values, ms can take the value + ½ or –½ :

ms = ½• Each atomic orbital can accommodate no more than two

electrons, one with ms= + ½ and another with ms= –½ .


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• Thus, each electron in an atom is described completely by a set of four quantum numbers: the first three describe its orbital, and the fourth describes its spin.


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• Spin is an intrinsic property of an electron and this is another quantum number besides the other three. This is not a property of the orbitals.

• A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected.

• Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction.



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week 1 quantum theory&atomic orbitals

Technology

atomic orbitals orbital

value of n

atoms orbitals

number of n value

quantum mechanics

principal quantum number

p orbitals

d orbitals