1. Electronic Structure of Atoms
Chapter 6
Copyright © The McGraw-Hill Companies, Inc.  Permission required for reproduction or display.

2. Waves
To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.
The distance between corresponding points on adjacent waves is the wavelength ().

3. Waves
The number of waves passing a given point per unit of time is the frequency ().
For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

4. Electromagnetic Radiation
All electromagnetic radiation travels at the same velocity: the speed of light (c),  108 m/s.
Therefore,
c: speed of light (3.00  108 m/s)
: wavelength (m, nm, etc.)
: frequency (Hz)
c = 

5. Sample Problems
The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?
A laser used to weld detached retinas produces radiation with a frequency of 4.69 x 1014 s-1. What is the wavelength of this radiation?

6. Max Planck and Quantized Energy
So an atom can change its energy by emitting or absorbing quanta
To understand quantization consider walking up a ramp versus walking up stairs:
For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height.

7. The Nature of Energy
Max Planck explained it by assuming that energy comes in packets called quanta.

8. The Nature of Energy
Einstein used this assumption to explain the photoelectric effect.
He concluded that energy is proportional to frequency:
E = h
where h is Planck’s constant,  10−34 J-s.
A change in an atom’s energy results in the gain or loss of “packets” of fixed amounts energy called a quantum.

9. Quantum staircase.

10. The Nature of Energy
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:
c = 
E = h

11. Sample Problem
Calculating the Energy of Radiation from Its
Wavelength
PROBLEM:
A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm. What is the energy of one photon of this microwave radiation?
PLAN:
After converting cm to m, we can use the energy equation, E = hn combined with n = c/l to find the energy.
SOLUTION:
E = hc/l
6.626X10-34J*s x
3x108m/s
E =
= 1.66x10-23J
10-2m cm
1.20cm

12. The Nature of Energy
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Electrons in an atom can only occupy certain orbits (corresponding to certain energies).
Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E = h

13. Schrodinger Wave Equation
Quantum Numbers and Atomic Orbitals
An atomic orbital is specified by three quantum numbers.
n the principal quantum number - a positive integer, indicates the relative size of the orbital or the distance from the nucleus.
The values of n are integers ≥ 1
l the angular momentum quantum number - an integer from 0 to n-1, related to the shape of the orbital
ml the magnetic moment quantum number - an integer from -l to +l, orientation of the orbital in the space around the nucleus 2l + 1
Ms spin quantum number
ms = +½ or -½

14. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l = 0, 1, 2, 3, … n-1
l = s orbital
l = p orbital
l = d orbital
l = f orbital
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
Value of l 1 2 3
Type of orbital s p d f
7.6

15. s Orbitals The value of l for s orbitals is 0.
They are spherical in shape.
The radius of the sphere increases with the value of n.

16. p Orbitals The value of l for p orbitals is 1.
They have two lobes with a node between them.

17. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
magnetic quantum number ml
for a given value of l
ml = -l, …., 0, …. +l
if l = 1 (p orbital), ml = -1, 0, or 1
if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2
orientation of the orbital in space
7.6

18. ml = -1
ml = 0
ml = 1
ml = -2
ml = -1
ml = 0
ml = 1
ml = 2
7.6

19. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
spin quantum number ms
ms = +½ or -½
ms = +½
ms = -½
7.6

20. Gives you the shape of the subshell
Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom.
number of electrons
in the orbital or subshell
1s1
principal quantum
number n
angular momentum
quantum number l
Gives you the shape of the subshell
Orbital diagram
1s1 H
7.8

21. “Fill up” electrons in lowest energy orbitals (Aufbau principle)? ?
Li 3 electrons
Be 4 electrons
C 6 electrons
B 5 electrons
B 1s22s22p1
Be 1s22s2
Li 1s22s1
H 1 electron
He 2 electrons
He 1s2
H 1s1
7.9

22. The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).
F 9 electrons
Ne 10 electrons
C 6 electrons
O 8 electrons
N 7 electrons
Ne 1s22s22p6
C 1s22s22p2
N 1s22s22p3
O 1s22s22p4
F 1s22s22p5
7.7

23. Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
7.7

24. Outermost subshell being filled with electrons
7.8

25. Not in your book. This edition took it out from the book
7.8

26. Energy of orbitals in a single electron atom
Energy only depends on principal quantum number n
n=3
n=2
n=1
7.7

27. Energy of orbitals in a multi-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 1
n=3 l = 0
n=2 l = 1
n=2 l = 0
n=1 l = 0
7.7

28. Schrodinger Wave Equation
Y = fn(n, l, ml, ms)
Existence (and energy) of electron in atom is described
by its unique wave function Y.
Pauli exclusion principle - no two electrons in an atom
can have the same four quantum numbers.
Each seat is uniquely identified (E, R12, S8)
Each seat can hold only one individual at a time
7.6

29. The Hierarchy of Quantum Numbers for Atomic Orbitals
Name, Symbol
(Property)
Allowed Values
Quantum Numbers
Principal, n
(size, energy)
Positive integer
(1, 2, 3, ...) 1 2 3 1 2
Angular momentum, l
(shape)
0 to n-1 1 +1 +2 -1 -2 -1 +1 -1 +1
Magnetic, ml
(orientation)
-l,…,0,…,+l