Download PERIODICITY AND ATOMIC STRUCTURE CHAPTER 5

PERIODICITY AND ATOMIC STRUCTURE
CHAPTER 5
How can we relate the structure of the atom to the way that it behaves chemically? The process of
understanding began with a realization that many of the properties of the elements show
periodicity when plotted against atomic number (originally against atomic weight).
The early periodic table based on atomic weight.
(Section 5.1)
Lets review:
What is a hydrogen atom?
e¯
1 electron
* nucleus H
1 proton
Experience has shown that the chemistry of the elements has nothing much to do with the nucleus
but is dominated by the behaviour of the electrons outside. It would be useful if there was some
way that the properties of these electrons could be examined.
5.1
One obvious method is to probe the electron cloud by removing electrons. There are several
different ways that this can be done. If an atom is bombarded with electrons of sufficient energy
two electrons will be ejected after the collision. Electrons can also be ejected by a beam of light of
a suitable colour (or energy usually written as hν because this is the energy of a light photon, E =
hν where h is Planck’s constant and ν is the frequency of the light).
Ionization Energy
e¯
light ( )
2e¯
e¯
First I.E.
Energy + M(g)
+
M(g) + e¯
+
2+
M(g)
M(g) + e¯
2+
3+
M(g)
M(g) + e¯ etc.
X
X X
X
X X X
X
X
XX X
X
X
k
X
X
n=1
X
X
l
m
n=2
SHELLS
n=3
The FIRST IONIZATION ENERGY is defined as the energy required to remove the least tightly held
electron from from one mole of gaseous atoms as defined by the reaction (where M represents an element).
M(g) → M+(g) + e¯
The SECOND IONIZATION ENERGY is defined as the energy required to remove the least tightly held
electron from from one mole of gaseous monopositive ions as defined by the reaction (where M represents
an element).
M+(g) → M2+(g) + e¯
The THIRD IONIZATION ENERGY is defined as the energy required to remove the least tightly held
electron from from one mole of gaseous dipositive ions as defined by the reaction (where M represents an
element).
M2+(g) → M3+(g) + e¯
First Ionization Energies for the Elements Z= 1 to 20
5.2
First Ionization Energies
The Successive Ionization Energies for the Third Row Elements
The successive ionization energies for sodium
Na
Sucessive Ionization Energies
Lg(kJ per mole)
5.5
5
4.5
4
3.5
3
2.5
1
2
3
4
5
6
7
8
Number of electrons removed
5.3
9
10
11
Wave Theory
Light
Light consists of electromagnetic radiation that exhibits wave like properties.
The velocity of light, c, is 2.998 x 108 m s-1 (roughly 3 x 1010 cm s-1) and is a constant for most
purposes. The velocity of light, c, can be related to the wavelength and frequency through the
expression:
c = νλ
Light also has some particle properties and is quantized. We can view the particle a the size of
the particle, called a photon, in terms of energy. The higher the frequency the greater the energy
associated with the light. The energy can be related to the frequency as follows:
Energy= E = hν
h is the Planck Constant = 6.626 x 10-34 J s
5.4
Atomic Spectra
The rainbow that we see on wet days is a continuous spectrum (remember Richard of York gained
battles in vain!) with no dark spaces in the spectrum. The elements emit light when heated and
absorb light when irradiated. The spectrum of the emitted light is not continuous but instead
consists of a series of distinct lines (hence the name Line Spectra).
An Emission Spectrum
An Absorption Spectrum
Hydrogen Spectrum
Balmer, by trial and error, found that,the frequencies of the four lines could be expressed by the
1
1
function ν= Rc( 2 2 − n 2 ) where n is an integer > 2 and R is a constant (the Rydberg Constant)
In fact there are more lines than the four shown. The four sets of lines are in different parts of the
spectrum. The Lyman series (UV), Balmer series (visible), the Paschen (infrared), Brackett and
Pfund!
1
ν= Rc( m 2
5.5
−
1
n2 )
The modern theory for the structure of the electron is derived from WAVE THEORY as applied to
the behaviour of electrons in atoms. Based on the wave theory the electron can be described in
terms of the (Schrödinger) Wave Equation and from the solution to the wave equation we can
determine the probability of finding an electron in any part of space. In fact there is a probability of
finding the electron anywhere but a greater probability of finding it near the nucleus. In terms of
the volume of space the probability reaches a maximum at the distance of the orbits (H, K, L, M).
In order to solve the wave equation various constants must be defined. These are called quantum
numbers and they ultimately define the energies of the various ORBITALS. The term orbitals is
used because they do not represent orbits (the Heisenberg uncertainty principle forbids that!) but
rather a probability envelope within which there is a certain probability of finding the electron.
Principal Quantum Number, n
This can take any integer value 1,2,3,4,5,6, etc
The Angular Momentum Quantum Number, l
This can take integer values 0,1,2,3 ... n-1
The Magnetic Quantum Number, ml
This can take integer values -l .... 0 .... l
The Spin Quantum Number, ms.
(Comes from experimental work rather than solving the equation)
This can have values - ½ or + ½
So on earth what does this all mean?
The chart shows the possible orbitals for each value of n - there are in fact n2 for each value of n
and for n=1 this gives only one orbital - and l = 0.
5.6
The energies of the obitals for the hydrogen atom are shown in the diagram (a) and for a
multielectron atom (b):
For the hydrogen atom the sub-levels are degenerate (have the same energy) but for multi
electron atoms the electrons interact and the sub-levels have different energies. The orbital type
for l = 0 is an s-orbital. The s-orbitals have electron density distributed equally in all directions
(spherically symmetrical) with the maximum density being at the distance of the old “orbit”.
Since the electron may be anywhere, we draw an envelope containing the space within which the
electron is 90% sure to be found. In this case the shape turns out to be a sphere. The greater the
value of n the larger the sphere.
S-orbitals - spherical. (the s actually means SHARP, a spectroscopic term)
For every value of n there is one s-orbital and they are designated as
1s, 2s, 3s, ...... ns.
Because, the electrons in an orbital can have ms, spin = +½ or -½ two electrons can be
accomodated in an orbital such that they do not have the same four quantum numbers. Hence, the
s-orbital can hold two electrons. We can now see why the n=1 (K shell) holds only two electrons
...
Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum numbers.
5.7
When ll=1, ml can have three values, -1, 0, +1 leading to three obitals each of which can hold two
electrons for a total of 6 electrons). These are called p-orbitals (p from principal) that belong to
what are called sub-levels (for each level of n there are n sub-level groups). The p-orbitals are
mutually at right angles:
When l =2, ml can have five values, -2, -1, 0, +1, +2 leading to five obitals each of which can hold
two electrons (total = 10 electrons). These are called d-orbitals (d for diffuse), the d sub-level and
havee more complicated shapes:
When l=3, ml can have seven values, -3, -2, -1, 0, +1, +2, +3 leading to 7 obitals each of which
can hold two electrons (for a total of 14 electrons). These are called f-orbitals (f for fundamental),
the f sub-level. The d-orbitals are even more complicated shapes.
While the calculations allow other values of l they are of no importance to us.
Now lets have another look at the way that the line spectrum is formed. The energy levels are not
equally spaced. Energy is released as excited electrons relax from higher levels to lower levels the lowest being for n = 1.
1
k
=R
1
m2
−
1
n2
5.8
see page 181
So which orbitals do the electrons
normally occupy?
The Aufbau (ger: building up)
Principle
In the GROUND STATE (the normal lowest energy state) the electrons
occupy orbital of the lowest possible
energy. Those electrons that are
nearest the nucleus have the lowest
energy and are the most tightly held
and require the largest amount of
energy to remove them. The highest
energy electrons will be most easily
removed.
The Pauli Exclusion Principle dictates
the number of electrons per shell.
H
Number of electrons
1
1s1
1s
↑
He
2
1s2
↑↓
5.9
The three orbitals in the p-sublevel all have the same energy (they are said to be degenerate) so
where do the electrons go?
Hund’s Rule
If two or more orbitals are available with the same energy, one electron goes into each, with
parallel spins (same ms), until all are half filled. Only then will spin pairing will take place.
We can now build up more elements:
H
Number of
electrons
1
1s1
↑
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
2
3
4
5
6
7
8
9
10
11
12
13
14
1s2
1s2 2s1
1s2 2s2
1s2 2s2 2p1
1s2 2s2 2p2
1s2 2s2 2p3
1s2 2s2 2p4
1s2 2s2 2p5
1s2 2s2 2p6
1s2 2s2 2p6 3s1
1s2 2s2 2p6 3s2
1s2 2s2 2p6 3s2 2p1
1s2 2s2 2p6 3s2 2p2
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
1s
Memory Aid - Nemonic
Examples
phosphorus, P
1s2 2s22p6 3s23p3
bromine, Br
1s2 2s22p6 3s23p63d10 4s24p5
5.10
2p
↑
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑
↑
↑
↑
↑
↑
↑↓ ↑
↑
↑↓ ↑↓ ↑
↑↓ ↑↓ ↑↓
EXCEPTIONS: Transition elements
Using these rules we can safely write electron configurations for the s- and p-block elements and
most of the d-block up to element 88. After that the energy levels get so close together that there
many exceptions. Knowing the electron configuration can help us understand the chemistry of the
elements. First we should look at the s- and p-block. If we examine the ions that these elements
form it is a simple matter to correlate the ion formation with the electron configuration. Now to
Chapter 6.
5.11