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Quantum Theory and the Electronic Structure of

Atoms

Chapter 7

Properties of Waves

Wavelength (l) is the distance between identical

points on successive waves.

Amplitude is the vertical distance from the

midline of a wave to the peak or trough.

7.1

Properties of Waves

Frequency (n) is the number of waves that pass

through a particular point in 1 second (Hz 1

cycle/s).

The speed (u) of the wave l x n

7.1

Maxwell (1873), proposed that visible light

consists of electromagnetic waves.

Electromagnetic radiation is the emission and

transmission of energy in the form of

electromagnetic waves.

Speed of light (c) in vacuum 3.00 x 108 m/s

All electromagnetic radiation l x n c

7.1

7.1

l x n c

l c/n

l 3.00 x 108 m/s / 6.0 x 104 Hz

l 5.0 x 103 m

l 5.0 x 1012 nm

7.1

Mystery 1, Black Body ProblemSolved by Planck

in 1900

Energy (light) is emitted or absorbed in discrete

units (quantum).

E h x n Plancks constant (h) h 6.63 x 10-34

Js

7.1

Mystery 2, Photoelectric EffectSolved by

Einstein in 1905

hn

- Light has both
- wave nature
- particle nature

KE e-

Photon is a particle of light

hn KE BE

KE hn - BE

7.2

E h x n

E h x c / l

E 6.63 x 10-34 (Js) x 3.00 x 10 8 (m/s) /

0.154 x 10-9 (m)

E 1.29 x 10 -15 J

7.2

7.3

7.3

Bohrs Model of the Atom (1913)

THIS CALCULATION HAS BEEN REMOVED

- e- can only have specific (quantized) energy

values - light is emitted as e- moves from one energy

level to a lower energy level

n (principal quantum number) 1,2,3,

RH (Rydberg constant) 2.18 x 10-18J

7.3

7.3

THIS CALCULATION HAS BEEN REMOVED

Ephoton DE Ef - Ei

7.3

THIS CALCULATION HAS BEEN REMOVED

Ephoton 2.18 x 10-18 J x (1/25 - 1/9)

Ephoton DE -1.55 x 10-19 J

Ephoton h x c / l

l h x c / Ephoton

l 6.63 x 10-34 (Js) x 3.00 x 108 (m/s)/1.55 x

10-19J

l 1280 nm

7.3

De Broglie (1924) reasoned that e- is both

particle and wave.

2pr nl l h/mu u velocity of e- m mass

of e-

THIS CALCULATION HAS BEEN REMOVED

7.4

THIS CALCULATION HAS BEEN REMOVED

l h/mu

m in kg

h in Js

u in (m/s)

l 6.63 x 10-34 / (2.5 x 10-3 x 15.6)

l 1.7 x 10-32 m 1.7 x 10-23 nm

7.4

Chemistry in Action Element from the Sun

In 1868, Pierre Janssen detected a new dark line

in the solar emission spectrum that did not match

known emission lines

Mystery element was named Helium

In 1895, William Ramsey discovered helium in a

mineral of uranium (from alpha decay).

Chemistry in Action Laser The Splendid Light

Laser light is (1) intense, (2) monoenergetic,

and (3) coherent

Chemistry in Action Electron Microscopy

le 0.004 nm

STM image of iron atoms on copper surface

Schrodinger Wave Equation

- In 1926 Schrodinger wrote an equation that

described both the particle and wave nature of

the e- - Wave function (Y) describes
- . energy of e- with a given Y
- . probability of finding e- in a volume of space
- Schrodingers equation can only be solved exactly

for the hydrogen atom. Must approximate its

solution for multi-electron systems.

7.5

QUANTUM NUMBERS

- The shape, size, and energy of each orbital is a

function of 3 quantum numbers which describe the

location of an electron within an atom or ion - n (principal) --- energy level
- l (orbital) --- shape of orbital
- ml (magnetic) --- designates a particular

suborbital - The fourth quantum number is not derived from the

wave function - s (spin) --- spin of the electron

(clockwise or counterclockwise ½ or ½)

Schrodinger Wave Equation

Y fn(n, l, ml, ms)

principal quantum number n

n 1, 2, 3, 4, .

distance of e- from the nucleus

7.6

7.6

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 0 s orbital l 1 p orbital l 2

d orbital l 3 f orbital

n 1, l 0 n 2, l 0 or 1 n 3, l 0, 1,

or 2

Shape of the volume of space that the e-

occupies

7.6

Types of Orbitals (l)

s orbital

p orbital

d orbital

7.6

p Orbitals

- this is a p sublevel with 3 orbitals
- These are called x, y, and z

There is a PLANAR NODE thru the nucleus, which is

an area of zero probability of finding an electron

3py orbital

p Orbitals

- The three p orbitals lie 90o apart in space

7.6

f Orbitals

- For l 3, f sublevel with 7 orbitals

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

ml -1

ml 0

ml 1

ml -2

ml -1

ml 0

ml 1

ml 2

7.6

Schrodinger Wave Equation

Y fn(n, l, ml, ms)

spin quantum number ms

ms ½ or -½

ms -½

ms ½

7.6

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

7.6

Schrodinger Wave Equation

Y fn(n, l, ml, ms)

Shell electrons with the same value of n

Subshell electrons with the same values of n

and l

Orbital electrons with the same values of n, l,

and ml

If n, l, and ml are fixed, then ms ½ or - ½

Y (n, l, ml, ½)

or Y (n, l, ml, -½)

An orbital can hold 2 electrons

7.6

If l 1, then ml -1, 0, or 1

2p

3 orbitals

If l 2, then ml -2, -1, 0, 1, or 2

3d

5 orbitals which can hold a total of 10 e-

7.6

Orbital Diagrams Energy of orbitals in a

multi-electron atom

Energy depends on n and l

7.7

Fill up electrons in lowest energy orbitals

(Aufbau principle)

Li 3 electrons

Be 4 electrons

B 5 electrons

C 6 electrons

Li 1s22s1

Be 1s22s2

B 1s22s22p1

H 1 electron

He 2 electrons

H 1s1

He 1s2

7.7

C 6 electrons

N 7 electrons

O 8 electrons

F 9 electrons

Ne 10 electrons

C 1s22s22p2

N 1s22s22p3

O 1s22s22p4

F 1s22s22p5

Ne 1s22s22p6

7.7

Order of orbitals (filling) in multi-electron atom

1s 5p

7.7

Why are d and f orbitals always in lower energy

levels?

- d and f orbitals require LARGE amounts of energy
- Its better (lower in energy) to skip a sublevel

that requires a large amount of energy (d and f

orbtials) for one in a higher level but lower

energy - This is the reason for the diagonal rule! BE SURE

TO FOLLOW THE ARROWS IN ORDER!

Electron configuration is how the electrons are

distributed among the various atomic orbitals in

an atom.

1s1

Orbital diagram

H

7.8

Mg 12 electrons

1s

1s22s22p63s2

2 2 6 2 12 electrons

Abbreviated as Ne3s2

Ne 1s22s22p6

Cl 17 electrons

1s

1s22s22p63s23p5

2 2 6 2 5 17 electrons

Last electron added to 3p orbital

n 3

l 1

ml -1, 0, or 1

ms ½ or -½

7.8

Outermost subshell being filled with electrons

7.8

Paramagnetic

Diamagnetic

unpaired electrons

all electrons paired

7.8

7.8

Exceptions to the Aufbau Principle

- Remember d and f orbitals require LARGE amounts

of energy - If we cant fill these sublevels, then the next

best thing is to be HALF full (one electron in

each orbital in the sublevel) - There are many exceptions, but the most common

ones are - d4 and d9
- For the purposes of this class, we are going to

assume that ALL atoms (or ions) that end in d4 or

d9 are exceptions to the rule. This may or may

not be true, it just depends on the atom.

Exceptions to the Aufbau Principle

- d4 is one electron short of being HALF full
- In order to become more stable (require less

energy), one of the closest s electrons will

actually go into the d, making it d5 instead of

d4. - For example Cr would be Ar 4s2 3d4, but since

this ends exactly with a d4 it is an exception to

the rule. Thus, Cr should be Ar 4s1 3d5. - Procedure Find the closest s orbital. Steal one

electron from it, and add it to the d.

Try These!

- Write the shorthand notation for
- Cu
- W
- Au

Ar 4s1 3d10 Xe 6s1 4f14 5d5 Xe 6s1 4f14 5d10

Exceptions to the Aufbau Principle

- The next most common are f1 and f8
- The electron goes into the next d orbital
- Example
- La Xe6s2 5d1
- Gd Xe6s2 4f7 5d1

Keep an Eye On Those Ions!

- Electrons are lost or gained like they always are

with ions negative ions have gained electrons,

positive ions have lost electrons - The electrons that are lost or gained should be

added/removed from the highest energy level (not

the highest orbital in energy!)

Keep an Eye On Those Ions!

- Tin
- Atom Kr 5s2 4d10 5p2
- Sn4 ion Kr 4d10
- Sn2 ion Kr 5s2 4d10
- Note that the electrons came out of the highest

energy level, not the highest energy orbital!