Lecture 5
Building the Atom Part II
Moseley’s Law
Pauli’s Exclusion Principle
The Periodic Table
Chemistry in two slides
Fyu02- Kvantfysik
David Milstead
What do we know so far ?
Electrons are arranged in shells with quantum number n
and have a fixed energy En
Within a shell electrons possess a value of orbital angular momentum
L = l(l +1)hFor any value of L there are 2l+1 possible states for an electron to
occupy.
Electrons also possess spin angular momentum and there are two
possible spin states for an electron.
S = s(s +1)hWe can now start to build and understand the periodic table!
Fyu02- Kvantfysik
David Milstead
X-Ray Lines
Accelerate and fire high energy (30-50keV) electrons
onto a heavy metal target and a characteristic X-ray
pattern is produced.
(1) Continuous radiation above a minimum wavelength
λ0 is observed. λ0 is independent of the target material.
(2) Sharp peaks, line spectra, are also observed which do
depend on the target material.
Fyu02- Kvantfysik
David Milstead
(1) In the presence of an atom electrons can lose energy
via bremsstrahlung (braking radiation) photons are emitted
over a continuous range of energy.
target atom
eγ
The photon energy can never exceed the electron energy.
Since E = hf
A maximum value of light frequency and
a minimum value of wavelengt h λ0 .
Energy of electron = eV
V = potential difference used to accelerate electron
hc
λ0 =
(5.1)
eV
Fyu02- Kvantfysik
David Milstead
Animation of elctrons emitting X-rays
through bremsstrahlung
http://www.launc.tased.edu.au/online/sciences/physics/Xrays.html
Fyu02- Kvantfysik
David Milstead
Line Spectra From X-rays
(2) The high energy electron interacts with an electron in a shell,
kicking it out. An electron from a higher shell moves
down to fill the hole, emitting a photon as it does so.
n=4 (N-shell)
K lines for transitions to n=1
L lines for transitions to n=2
M lines for transitions to n=3
N lines for transitions to n=4
n=3 M-shell)
Lα
Kα
Kβ
Lβ
n=2 (L-shell)
Kγ
n=1 (K-shell)
Line spectra are characteristic for different atoms!
Fyu02- Kvantfysik
David Milstead
Moseley’s Law
Moseley noted that lines shift systematically as
target material changes.
”We have proof that there is a
1
9
f × 10 Hz 2
fundamental quantity which
changes by regular steps as
3.0
we pass from one element to
the next. This quantity
2.0
must be the charge on the nucleus”
1.0
Moseley'
s Law
f Kα = a( Z − 1) (5.2)
a = constant
Kα transition
Fe +Co
Ti + +
K +Cr
+ +
Al
5 10 15 20 25 30 35 40
Atomic number Z
Fyu02- Kvantfysik
David Milstead
Question
A target is bombarded with 30-keV electrons. What is the minimum
wavelength in the continuous X-ray spectrum ?
Minimum wavelength λmin occurs at
maximum energy of radiated photon Emax
Emax = electron energy = 30 keV
E = 30 × 10 3 × 1.602 × 10 −19 = 4.81 × 10 −15 J
hc
E=
min
λmin
hc 6.63 × 10 −34 × 3 × 108
−11
=
4
.
14
×
10
m
=
=
−15
E
4.81 × 10
Fyu02- Kvantfysik
David Milstead
Moseley’s plot does not go through the origin. Why ?
Consider electron in innermost K shell (n=1) ejected by X-ray.
Electron from next highest state makes transition to fill ’hole’.
e’hole’
nucleus
Electron about to drop into
the hole in the K-shell ’sees’
an effective nuclear charge (Z-1)e
due to screening from remaining
K-shell electron.
Apply argument to Bohr theory and
obtain eqn 5.2.
Fyu02- Kvantfysik
David Milstead
Pauli’s Exclusion Principle
Electron states in all atoms classified by quantum numbers
n, l,ml, ms
Why do all electrons not simply fall to the ground state ?
Explained by:
Pauli Exclusion Principle
No two electrons in an atom can have the same four quantum
numbers n, l,ml, ms
Fyu02- Kvantfysik
David Milstead
Shells and subshells
Electrons fill shells (n) and subshells (l).
For each value of l, there are 2l+1 values of ml
Since ms=1/2 or –1/2 each subshell can have 2(2l+1 ) electrons
n
l
ml
1
0
0
±
1
2
K
1s
No. in
subshell
2
2
0
0
±
1
2
L
2s
2
2
1
±
1
2
L
2p
6
3
0
0
±
1
2
M
3s
2
3
1
0 ,± 1
±
1
2
M
3p
6
3
2
0 ,± 1,± 2
M
3d
10
0 ,± 1
ms
±
1
2
shell subshell
2
8
18
Fyu02- Kvantfysik
David Milstead
Animation of electrons in shells
http://www.colorado.edu/physics/2000/applets/a2.html
Fyu02- Kvantfysik
David Milstead
Filling Shells
1s
2s
2p
3s
3p
3d
4s
4p
4d
5s
5p
5d
6s
6p
6d
7s
In general for a given value of n, the energy
of the state increases with l
Example:
energy of 4s < energy of 4l < energy of 4d
4f
However a new shell can start to be filled before
the old shell is full.
5f 5g Example: the 4s state is lower than the 3d state
and is filled first.
Guide (left) indicates (roughly) how shells
are filled.
Fyu02- Kvantfysik
David Milstead
Periodic Table in terms of Shells
Halogens
period
Periods of 2,6,8,8,18 electron states
Noble gases
Alkali
Metals
Fyu02- Kvantfysik
David Milstead
Periodic Table in Terms of
Elements
Fyu02- Kvantfysik
David Milstead
Interactive Periodic Table of the Elements with Properties
http://www.beta-theta.com/Chemistry/Period.html
Fyu02- Kvantfysik
David Milstead
Describing electron
configurations in atoms
Write down the filled subshells nbc
n=principal quantum number
b=subshell s,p,d,f…
c=number of electrons in subshell
What is the electron configuration for the element niobium ?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d3
What is the electron configuration for the element nickel (28) ?
1s2 2s2 2p6 3s2 3p6 4s2 3d8
Fyu02- Kvantfysik
David Milstead
Chemistry in two slides
Explain chemical properties of elements from filling shells and
subshells
(1) Noble gases (He, Ar, ..) have p shells filled – stable
(2) Alkali metals (Li,Na,K..) have a single loosely bound
electron in outer p-shell – very reactive
(3) Halogens (F, Cl, Br…) miss one electron in their p-shells
- energetically favourable to take an electron from an alkali metal
to form a compound. Example, NaCl.
Fyu02- Kvantfysik
David Milstead
Ionisation energy is largest
For the noble gases
and lowest for the akali metals
Atomic radius large for
Alkali metals and small for
noble gases
Increasing nuclear charge
pulls electrons in the same
shell closer to the nucleus
Electron
occupies
a new shell
at larger radius
Fyu02- Kvantfysik
David Milstead
Atomic radii in pm