Download Structure of atoms and solids

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FROM IDEAS TO IMPLEMENTATION
9.4.3
ATOMS TO TRANSISTORS
STRUCTURE OF ATOMS AND SOLIDS
STRUCTURE OF THE ATOM
In was not until the early 1930’s that scientists had fully developed a model of the
atom based upon quantum physics and that was supported by experimental evidence
based upon the existence of the electron, proton and neutron. Atoms consist of a
positive nucleus containing protons (positive) and neutrons (neutral). The radius of a
nucleus is about 10-15 m. Most of the mass of the atom is due to the nucleus. Electrons
being negatively charged are bound to the positively charged nucleus. Typical radii for
atoms are about 10-10 m. The number of protons within a nucleus determines the
element. For example, carbon: 12 protons and uranium: 92 protons.
The electrons are not like planets orbiting the Sun. In quantum physics terms, the
bound electrons behave as waves and it is only possible to determine the probability of
finding the electron within a small volume. The notion of a trajectory for these
electrons is meaningless. The best way to visualize an atom is to think of a small
nuclear core embedded in a an electron cloud where at certain locations there is zero
probability of finding the electron while at other locations there is a high probability.
Probability cloud for a hydrogen atom
(2s electron)
high probability of finding electron
zero probability of finding an electron
10x10-10 m
Probability cloud for a hydrogen atom
(4d electron)
high probability of finding electron
zero probability of finding an electron
50x10-10 m
Fig. 1. Electron probability clouds for a hydrogen atom.
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All the information about electrons in an atom is given by a set of four quantum
numbers. This set of four numbers determines the state of the atom and this tells us
all we can know about the electrons.
Principle quantum number (shell)
n = 1, 2, 3, …
Orbital quantum number (subshell) l = 0 (s), 1 (p), 2 (d), … , n-1
Magnetic quantum number
ml = 0, 1, … , l
Spin quantum number
m s =  1/2
Each electron in an atom has a unique set of these four quantum numbers (Pauli
Exclusion Principle). Electrons in an atom have their total energy (kinetic + potential)
quantized. For a given atom, there is a set of discrete energy values that the electrons
bound to the nucleus can possess. These discrete energy levels are classified by shells
(labelled n = 1, 2, 3, …) and subshells (labelled s, p, d, …). These energy levels
determine the electronic configuration for an atom. The lowest energy levels are filled
first by the electrons. The lowest energy state of an atom is called its ground state.
When an atom absorbs energy, electrons can jump only to vacant and available energy
levels (excited atoms).
The sodium atom (atomic number Z = 11) has 11 electrons. Its electronic configuration
can be written as
Na
Z = 11
1s2 2s2 2p6 3s1
excited
state
ground
state
total
energy
total
energy
3d
3d
4s
4s
3p
3p
3s
3s
2p
2p
2s
2s
1s
1s
not to scale
not to scale
atom can only absorb an
amount of energy equal
to the difference between
two energy levels
number of electrons
1s2 2s2 2p6 3s1
shell
subshell
Fig. 2. Energy levels for a sodium atom. The shells shown are n = 1, 2, 3, 4. The
subshells are s, p and d. The up arrow is for ms = +1/2 and the down arrow for ms
= - ½. Two electrons fill an s-subshell; six electrons fill a p-subshell and 10
electrons fill a d-subshell.
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STRUCTURE OF SOLIDS
Molecules and solids both exist by virtue of the strong interactions that occur between
their atoms. We shall see how quantum theory of the atom can be extended to
account for the electrical properties of solids and how this has led to the computer,
mobile phones and the internet revolution now happening. The basic building blocks
(computer chips, microchips, microprocessors, etc) perform the necessary operations
and calculations for devices such as computers and mobile phones. These basic
building blocks are constructed from semiconductor materials in which resistors,
capacitors, pn junctions and transistors are the fundamental components.
Most solids are crystalline in nature, with their constituent atoms arranged in regular,
repeated units. The ionic and covalent bonds between atoms that are responsible for
the formation of molecules also act to hold many crystalline solids together.
In ionic bonding, each ion (charged atom) attracts itself to as many ions of opposite
sign that can fit around it. The attraction between opposite charged ions balances the
repulsion between similar charged ions to given an equilibrium configuration. Figure 3
shows the ionic structure for a Na+Cl- crystal.
_
large chloride
negative ion
(Cl-)
_
+
+
small positive
sodium ion
(Na+)
Fig. 3. Ionic structure for Na+Cl- crystal.
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In covalent bonding crystals, the attractive interatomic forces holding the crystal
together arise from the sharing of electrons between atoms. For example, in diamond,
the carbon atoms share electron pairs with the four other carbon atoms adjacent to it.
All the electrons in the outer shells of the carbon atoms participate in the binding
(electron configuration of carbon 1s2 2s2 2p2). This structure is the reason why
diamond is extremely hard and it must be heated to a temperature greater than
~3000 oC before its crystal structure is disrupted. All the electrons are tightly bound to
carbon atoms, so very few electrons are mobile, hence, diamond is a very good
electrical insulator.
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
carbon – diamond structure:
each carbon atoms shares a
pair of electrons with four
neighbouring carbon atoms
Fig. 4. Covalent structure of diamond. Each carbon atom shares electron pairs
with four adjacent carbon atoms.
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Metallic bonding is another very important way in which solids can be held together
by strong cohesive forces. A characteristic property of all metal atoms is the presence
of only a few electrons in their outer shells, and these electrons can be detached
relatively easily to leave behind a positive ion. A useful model of a metal in a solid state
is to consider the solid to be an assembly of atoms that have given up their outer most
electrons to form an electron gas of freely moving electrons that pervades the entire
metal. The electrostatic interaction between the positive cores (nuclei + bound
electrons) and the free negative electrons holds the metal together.
positive core (nucleus + bound electrons)
The repulsion between the
positive cores is balanced by the
attractive forces with the
negative electron cloud
negative electron cloud
consisting of free electrons
that can easily move through
crystal structure
Fig. 5. The metallic bond
The high electrical and thermal conductivities of metals follows from the ability of
these free electrons to freely move throughout their crystal structure. This is not the
case in covalent or ionic bonding where electrons are tightly bound to single or groups
of atoms.
Unlike other crystals, metals may be deformed without breaking, because the electron
gas allows atoms to slide pass each other whilst maintaining their strength. It is easy to
make alloys (mixture of different metals) because of the non-specific nature of the
metallic bond. When electromagnetic radiation is incident upon a metal surface, the
free electrons start to vibrate because they absorb energy from the oscillating electric
and magnetic fields of the incident electromagnetic wave. These oscillating electrons
themselves act as sources of electromagnetic radiation, emitting the radiation in all
direction at the same frequency as the incident wave. Some of these waves produced
from the oscillating electrons will be emitted from the surface of the metal giving rise
to the metal surface having a lustrous appearance and also makes the metal a good
reflector. (N.B. in reflection from the metal surface, the incident radiation is absorbed,
and the emitted radiation is due to the oscillations of the free electrons.
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