Some final thoughts on the Bohr model Obviously the result obtained by Bohr was very useful to Schrödinger. Connection with Heisenberg Uncertainty Principle. According to Bohr, an electron is always circling around the nucleus in a well specified orbit. Although the electron may switch from one orbit to another, as in an emission or absorption process, its position in an orbit at a specific distance from the nucleus is fixed once we know its energy state.

A simplified Heisenberg argument.

A simplified Heisenberg argument A simplified Heisenberg argument. Suppose the energy of the electron in the H atom is all kinetic energy (the argument could be modified to take account that there is a second energy component).

A simplified Heisenberg argument A simplified Heisenberg argument. Suppose the energy of the electron in the H atom is all kinetic energy (the argument could be modified to take account that there is a second energy component). m2v2 p2 E = ½ m v2 = = 2m 2m

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0.

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0.

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0.

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. In other words, the electron cannot be in a well defined orbit!

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. In other words, the electron cannot be in a well defined orbit! The electron could be anywhere!!!!!

Now if E is known exactly, then so is p, hence the error in p is zero, so = 0. In other words, the electron cannot be in a well defined orbit! The electron could be anywhere!!!!! This is the death certificate of the Bohr model.

We learn from quantum theory that we should never think of the electron as being confined to a certain path.

We learn from quantum theory that we should never think of the electron as being confined to a certain path. It is more appropriate to speak of the probability of locating the electron in a certain region of space.

We learn from quantum theory that we should never think of the electron as being confined to a certain path. It is more appropriate to speak of the probability of locating the electron in a certain region of space. This probability is given by the square of the wave function.

Since the electron has no well-defined position in the atom, it is most convenient to use terms like:

Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density

Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density Electron Charge Cloud

Since the electron has no well-defined position in the atom, it is most convenient to use terms like: Electron density Electron Charge Cloud Charge Cloud to represent the probability concept.

To distinguish the quantum mechanical description from Bohr’s model, the word “orbit” is replaced with the term orbital or atomic orbital.

To distinguish the quantum mechanical description from Bohr’s model, the word “orbit” is replaced with the term orbital or atomic orbital. Atomic orbital means exactly the same as wave function describing one electron.

When we say that an electron is in a certain orbital, we mean that the distribution of the electron density or the probability of locating the electron in space is described by the square of the wave function associated with that energy state.

When we say that an electron is in a certain orbital, we mean that the distribution of the electron density or the probability of locating the electron in space is described by the square of the wave function associated with that energy state. For each atomic orbital, there is an associated energy as well as an associated electron density.

Quantum Numbers

Quantum Numbers From quantum mechanics it is found that four quantum numbers are necessary to describe the placement of electron(s) in the hydrogen atom or in any other atom.

Quantum Numbers From quantum mechanics it is found that four quantum numbers are necessary to describe the placement of electron(s) in the hydrogen atom or in any other atom. The quantum numbers are of significance if we wish to understand the sizes and shapes of orbitals and their associated energy levels.

These are important, because the size, shape, and energy of the electron cloud influence the behavior of atoms.

1. Principal quantum Number

1. Principal quantum Number Symbol n

1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that En ).

1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that En ). The principal quantum number also characterizes the “size” of the orbital.

1. Principal quantum Number Symbol n The principal quantum number determines the energy of an orbital (remember that En ). The principal quantum number also characterizes the “size” of the orbital. The larger the value of n, the larger the orbital, and the farther on the average the electron is from the nucleus.

Roughly speaking, the “size” of an orbital is proportional to n2 Roughly speaking, the “size” of an orbital is proportional to n2. As n increases, the “size” differences among orbitals becomes very large.

Roughly speaking, the “size” of an orbital is proportional to n2 Roughly speaking, the “size” of an orbital is proportional to n2. As n increases, the “size” differences among orbitals becomes very large. Because the “sizes” of orbitals with different n values differ so significantly, the regions of space corresponding to particular values of n are referred to as shells around the nucleus.

Shell K L M N O … n 1 2 3 4 5 …

2. The Angular Momentum Quantum Number Also called the azimuthal quantum number.

2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l

2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l The angular momentum quantum number determines the “shape” of the orbitals.

2. The Angular Momentum Quantum Number Also called the azimuthal quantum number. Symbol l The angular momentum quantum number determines the “shape” of the orbitals. The possible values of l depend on the value of the principal quantum number n.

For a given value of n, l takes values from 0 to n – 1 (in steps of 1).

n – 1 (in steps of 1). If n = 1, there is only one value of l, that is For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0

n – 1 (in steps of 1). If n = 1, there is only one value of l, that is For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0 If n = 2, there are two values of l, that is l = 0 and l = 1

n – 1 (in steps of 1). If n = 1, there is only one value of l, that is For a given value of n, l takes values from 0 to n – 1 (in steps of 1). If n = 1, there is only one value of l, that is l = n – 1 = 1 – 1 = 0 If n = 2, there are two values of l, that is l = 0 and l = 1 If n = 5, there are five values of l, that is l = 0, l = 1, l = 2, l = 3, l = 4

Each value of l for a given value of n defines a subshell.

Each value of l for a given value of n defines a subshell. The following letters are used as symbols to designate the different values of l.

Each value of l for a given value of n defines a subshell. The following letters are used as symbols to designate the different values of l. l value 0 1 2 3 4 5 … orbital designation s p d f g h ….

3. The Magnetic quantum Number

3. The Magnetic quantum Number Symbol ml

3. The Magnetic quantum Number Symbol ml This quantum number is used to explain the additional lines that appear in the spectra of atoms when they emit light while confined in a magnetic field.

The magnetic quantum number determines the orientation of the orbital in space.

The magnetic quantum number determines the orientation of the orbital in space. The value of ml depends on the value of l. For a given value of l there are 2l + 1 integer values of ml ranging from - l to l.

The magnetic quantum number determines the orientation of the orbital in space. The value of ml depends on the value of l. For a given value of l there are 2l + 1 integer values of ml ranging from - l to l. Examples: If l = 0, ml = 0

The magnetic quantum number determines the orientation of the orbital in space. The value of ml depends on the value of l. For a given value of l there are 2l + 1 integer values of ml ranging from - l to l. Examples: If l = 0, ml = 0 If l = 1, ml = -1, or 0, or 1

The magnetic quantum number determines the orientation of the orbital in space. The value of ml depends on the value of l. For a given value of l there are 2l + 1 integer values of ml ranging from - l to l. Examples: If l = 0, ml = 0 If l = 1, ml = -1, or 0, or 1 If l = 2, ml = -2, -1, 0, 1, 2

The number of different values that ml may take for a given subshell, indicates the number of individual orbitals.

The number of different values that ml may take for a given subshell, indicates the number of individual orbitals. Examples: If l = 0, there is one value for ml and only one orbital.

The number of different values that ml may take for a given subshell, indicates the number of individual orbitals. Examples: If l = 0, there is one value for ml and only one orbital. If l = 1, there are three values for ml and three orbitals.

4. The Electron Spin Quantum Number

4. The Electron Spin Quantum Number Symbol ms

4. The Electron Spin Quantum Number Symbol ms There are only two possible values for ms: ms = ½ or ms = - ½

4. The Electron Spin Quantum Number Symbol ms There are only two possible values for ms: ms = ½ or ms = - ½ To explain certain spectral lines from atoms in the presence of a magnetic field, it was found to be necessary to assume that electrons act as tiny magnets.