Chapter 5 Notes Dr. Floyd Beckford

The Electron Background: The existence of electrons had been known for a long time even though no hard experimental proof was available until the development of cathode ray tubes. These are tubes evacuated or containing gas at very low pressure. Two electrodes are also contained in the tube.

If a high voltage is applied to the tube, the cathode (which is the negative electrode) emits electrical particles that move towards the anode (the positive electrode). The nature of the particles was established by a series of experiments:

1. A fluorescent screen at the back of the tube glows when it is struck by the particles. This confirms the presence of the particles.
2. If a small object is place in the path of the beam, a shadow is cast. This means that the beam travels in a straight line from cathode to anode.
3. A pair of electrically charged plates is placed across the beam, it is deflected by the electrical field, towards the positive plate.
4. Application of a magnetic field causes deflection of the beam in a direction consistent with negative charges.
5. If a small paddle wheel is placed in the path of the beam, the wheel turns. This implies that the beam have mass.

It was therefore established that cathode rays is a beam of negatively charged particles called electrons.
By varying the electrical and magnetic fields, the charge (e) to mass (m) ratio (e/m) for electrons was established.

The Neutron
Because neutrons are not charged, they were the lasts to be discovered. They were discovered when beryllium was bombarded with alpha particles. (Alpha particles are actually He²⁺ ions).

How does the three fundamental particles relate spatially to each other in atoms?
Background: The initial theory was the so-called ‘plum pudding’ model. This is the view of the atom as a sea of positive charges with the negative charges embedded in this of positive charge.

The Nuclear Atom
A piece of thin gold foil is bombarded with a-particles (He²⁺). Most of the particles pass through the foil. Some are deflected through varying angles but most importantly some were deflected back towards the source. The results were analyzed as the following:
The scattering of the positive a-particles was caused by repulsion from very dense regions of positive charge in the gold foil. This is the like repels like theory.

The suggestion was that each atom contains a tiny, positively charged, dense center called the nucleus. The particles that were deflected were those that pass relatively close to the nucleus. Since the majority of particles pass right through, the atom must primarily be empty space, populated by the very light electrons.

This led to the formulation of the nuclear atom: Atoms consist of very small, very dense nuclei (containing protons and neutrons) surrounded by clouds of electrons at relatively great distances from the nuclei.

Atomic Number:
Each element differs from the preceding element by having one more positive charge in its nucleus. The number of protons in the nucleus is known as the atomic number. All atoms of an element have the same number of protons. The number of neutrons in the atom can and usually does vary however. Atoms that have the same number of protons but a different number of neutrons are called isotopes.

The composition of a nucleus is indicated by its nuclide symbol.

Mass Spectrometry and Isotopic Abundance
Mass spectrometers measure the charge-to-mass ratio of charged particles. In a spectrometer positive ions of a sample gas are created. The ions are subjected to, first an electric field and then a magnetic field. The magnetic field causes the ionic beam to be deflected. The magnitude of the deflection depends on:
1. The electric field strength; faster moving particles (higher voltages) are deflected less than slower moving particles (lower voltages).
2. Magnetic field strength; stronger fields deflect a given beam more than weaker fields. 3. Masses of the particles; heavier particles are deflected less than lighter particles assuming the charges are the same.
4. Charges on the particles; particles with higher charges are deflected more than particles with lower charges assuming the masses are the same.

From a mass spectrum, masses of isotopes as well as the relative amounts of the isotopes (isotopic abundance) can be obtained.

Wave nature of the Electron
We know that light behaves as waves as well as particles (photons). It was proposed that if electromagnetic waves can behave as particles, then small moving particles of matter may also have wave properties. The wave nature of very small particles can be expressed as the following relationship.

= h/mv (m = mass, v = velocity, h = Planck’s constant)

THE QUANTUM MECHANICAL ATOM
The theory of quantum mechanics is based on the wave nature of matter. In quantum mechanics we cannot tell exactly where the electron is inside the atom. This observation is stated as the Heisenberg Uncertainty Principle: It is impossible to determine accurately both the momentum and the position of an electron (or any other very small particle) simultaneously.
In practical terms the only thing we can do is calculate the probability of finding an electron with a given energy within a given region in space.

Basic ideas of quantum mechanics:
1. Atoms and molecules exist in quantized energy states. An atom or molecule emits or absorb the exact amount of energy to take it to the next energy level.
2. Atoms and molecules change their energies by emitting or absorbing energy.
3. The allowed energy states of atoms and molecules can be described by a set of numbers called quantum numbers.

Quantum mechanics is based chiefly on the Schrodinger Equation. Solutions of this equation are called wave functions and are used to describe the arrangement of electrons in atoms.
1. Only certain wave functions are possible because an atom’s energy is quantized.
2. Each wave function corresponds to an allowed energy for the electron.
3. Theoretically, an electron can be anywhere around a nucleus, but in reality it is very likely to within a certain region in space. These regions are called orbitals.
4. Orbitals can be mathematically organized using a set of three integers called quantum numbers. Each orbital has a unique set of quantum numbers.

Orbitals are classified in three ways:

Electron Shells; an electron shell (or energy level) is a collection of orbitals, identified by an integer, n, which ranges from 1 --> infinity. Electrons with the same value are in the same shell. The larger the value of n, the greater the average distance of the electron from the nucleus.
Subshells; (sub-levels) are groups of orbitals within an electron shell. They are identified by the letters s, p, d and f. The number of subshells is equal to the n value of the shell.
Orbitals; Individual orbitals are identified by their direction in space. The number of orbitals within a subshell depends on the subshell type: s subshells have a single orbital, p subshells have 3 orbitals, d subshells have 5 and f subshells 7 orbitals.

Quantum Numbers
Four quantum numbers are used to designate the electronic configuration of atoms. a. n, the principal quantum number, describes the main energy level and is the primary indicator of the energy of the electron.

The value of n, l and m_l describe a particular atomic orbital: each orbital can accommodate no more than two electrons, one with m_s = - 1/2 and m_s = + 1/2.

ATOMIC ORBITALS
Remember that each electron is said to occupy an atomic orbital defined by a set of four quantum numbers. We distinguish between orbitals in different principal shells by using the principal quantum number as coefficients: 1s indicates the s orbital in the first energy level; 2s is the s orbital in the second energy level; 3p is the p orbital in the third energy level, etc.

The maximum electron capacity of an orbital is equal to 2n². The lower the value of n, the closer is the electron to the nucleus and the more stable is the atom. After the first energy level (at n = 2), the atomic orbital contains a p sublevel, defined by l = 1. This means that each sublevel has three p orbitals defined by m_l = ± 1 i.e. -1, 0, +1. (Remember that m_l = ± l).

At the third energy level (n = 3), there is a third sublevel, l = 2, composed of five d atomic orbitals. l = 2, means m_l = ± 2 i.e. m_l = -2, -1, 0, 1, 2

At the fourth energy level, there is a fourth sublevel, l = 3, containing a set of seven f orbitals.

So far we have only seen three quantum numbers. The fourth quantum number, m_s = ± ½ indicates the spin of the electron. Two electrons in the same orbital having opposite ms values are said to be paired.

Electron Configurations
The ground state of an isolated atom is the state of lowest energy. The electron configuration of an atom in this state is the ground state electron configuration. Unless otherwise stated, this is the configuration normally written.

The guiding principle of building up electron configurations is the Aufbau Principle. This is based on the idea of creating the atom with the lowest total energy. To do this:
1. Find the right amount of electrons as dictated by the atomic number.
2. Placing these electrons in such a way as to give the lowest total energy atom.

Remember that orbitals increase in energy with increasing value of n. For each n, energy increases with the value of l. Therefore the s sublevel is lowest in energy, the p sublevel is the next lowest, then the d and f sublevels.

The electron structures of atoms are governed by the Pauli Exclusion Principle:
No two electrons in an atom may have identical sets of four quantum numbers

This means that no more than two electrons can occupy an atomic orbital and for two to share the same orbital, they must have opposite spins.

There are a number of ways to represent electron configurations. Using nitrogen as the example.
1. The spectroscopic notation: 1s² 2s²2p.
2. The orbital notation:
3. The noble gas notation: [He] 2s² 2p³

In the example above we see that we have three p orbitals of the same energy. These orbitals are said to degenerate. Placement of electrons in degenerate orbitals is dictated by Hund’s Rule: Electrons must occupy all the orbitals of given sublevel singly before pairing can begin. These unpaired electrons have parallel spin.
The reason for this is that paired electrons repel each other greater than do two unpaired electrons in different but degenerate orbitals.

In elucidating electron configurations of Row 4 & 5 elements, the (n + 1) rule dictates. This rule states that the (n + 1)s orbital, gets filled before the nd orbital. So the 4s orbital gets filled before the 3d orbital.