chapter 6: electronic structure of atoms light is a form of electromagnetic radiation (emr): an...

Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms

Light is a form of electromagnetic radiation (EMR):

• an oscillating charge, such as an electron, gives rise to electromagnetic radiation:

Electric Field

Magnetic Field


• Both the Electric and the Magnetic field propagate through space

• In vacuum, both move at the speed of light (3 x 108 m/s)


Electromagnetic radiation is characterized by

• wavelength (), or frequency ()

and

• amplitude (A)

A = intensity


Frequency measures how many wavelengths pass a point per second:

1 s


Electromagnetic radiation travels at the speed of light:

c = 3 x 108 m s-1

Relation between wavelength, frequency, and amplitude:

c =


400 nm 750 nm


Red Orange Yellow Green Blue Ultraviolet


What is the wavelength, in m, of radiowaves transmitted bythe local radio station WHQR 91.3 MHz?

c

c m29.3


A certain type of laser emits green light of 532 nm. What frequency does this wavelength correspond to?

c

c 1141064.5 s

Hz141064.5


Classically, electromagnetic radiation (EMR) was thought to have only wave-like properties.

Two experimental observations challenged this view:

Blackbody radiation

Photoelectric Effect


Blackbody radiation

• Hot objects emit light

• The higher T, the higherthe emitted frequency


Blackbody radiation

Brightness

wavelength ()

visible region

T2

T1

prediction of classical theory

= there would be NO DARKNESS

“ultraviolet catastrophe”


Blackbody radiation

• light is emitted by oscillators

• high energy oscillators require a minimum amount of energy to be excited:

E = h

• energy is not provided by temperature in “black body”

Max Planck (1858 - 1947)


Blackbody radiation

E = h

Planck’s constant = 6.63 x 10-34 J s

frequency of oscillator

Energy of radiation is related to frequency, not intensity


What is the energy of a photon of electromagnetic radiation that has a frequency of 400 kHz?

hE

= 2.65 x 10-28 J



Albert Einstein (1879-1955)

e- e- e-



Albert Einstein (1879-1955)

e- e- e-

e-

• Light of a certain minimum frequency is required to dislodge electrons from metals



• Ability of light to dislodge electrons from metals is related to its frequency, not intensity

E = h

• This means that light comes in “units” of h

• The h “unit” is called a quantum of energy

• A quantum of light (EMR) energy = photon

• Intensity is related only to the number of “units”


Relationship between Energy, Wavelength, and Frequency:

c hE

c

hE

hEc

ch

E


What is the energy of a photon of light of 532 nm?

ch

E

= 3.74 x 10-19 J


or

E = h

Electromagnetic Radiation

wavestream of particles

(photons)

Whether light behaves as a wave or as a stream of photons depends on the method used to investigate it !


Understanding light in terms of photons helped understand atomic structure

many light sources produce a continuous spectrum


Thermally excited atoms in the gas phase emit line spectra

continuous spectrum (all wavelengths together: white light)

line spectrum (only some wavelengths: emission will have a color)


Photograph of the H2 line spectrum (Balmer series) in the visible region

(1825-1898)

Johann Balmer (1825-1898)

2

2

2

1

111nn

RH

Rydberg constant1.097 x 107 m-1 positive integers

(e.g. 1,2,3, etc)


Niels Bohr was the first to offer an explanation for line spectra

Bohr Model of the Hydrogen Atom

• Only orbits of defined energy and radii are permitted in the hydrogen atom

• An electron in a permitted orbit has a specific energy and will not radiate energy and will not spiral into the nucleus

• Energy is absorbed or emitted by the electron as the electron moves from one allowed orbit into another. Energy is absorbed or emitted as a photon of E = h


Niels Bohr was the first to offer an explanation for line spectra

(1885-1962)

electron orbits

Bohr’s Model of the Hydrogen Atom

n = 1n = 2n = 3n = 4n = 5n = 6

nucleus



n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

eabsorption of a photon



n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

e



n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

e “excited state”



n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

e



n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

e emission of a photon


n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

nucleus

(a) (b) (c)

Which of these transitions representsan absorption process?

Which of these transitions involves thelargest change in energy?

Which of these transitions leads to theemission of the longest wavelength photon?

Does this wavelength correspond to a high or low frequency?


Transitions corresponding tothe Balmer series


n = 6n = 5n = 4

n = 3

n = 2

n = 1

n = Principal Quantum Number (main energy levels)

4

11018.2 18 JE

JE 181018.2

9

11018.2 18 JE

Energy of electron in a given orbit:

2

1n

RchE H

h=Planck’s constant, c=speed of light, RH = Rydberg constant


n = 6n = 5n = 4

n = 3

n = 2

n = 1

2

1

final

Hfinal nRchE

For an electron moving from n = 4 to n = 2:

2

1

initial

Hinitial nRchE

initialfinal EEE

22

11

initial

H

final

H nRch

nRchE

22

11

initialfinal

H nnRchE


n = 6n = 5n = 4

n = 3

n = 2

n = 1

For an electron moving from n = 4 to n = 2:

22

11

initialfinal

H nnRchE

22 4

1

2

1HRchE

16

1

4

11018.2 18 JE

1875.01018.2 18 JE

E = - 4.09 x 10-19 J


n = 6n = 5n = 4

n = 3

n = 2

n = 1

E = 4.09 x 10-19 J

What wavelength (in nm) does this energy correspond to?

ch

E Ech

JmsJs

19

1834

1009.41031063.6

The energy of the photon emitted is:

= 486 x 10-9 m

= 486 nm


n=6 → n=2

n=5 → n=2

n=4 → n=2 n=3 → n=2

Balmer Series

= 486 nm


The Wave Behavior of Matter

If light can behave like a stream of particles (photons)…

… then (small) particles should be able to behave like waves, too

vmh

For a particle of mass m, moving at a velocity v:

De Broglie Wavelength

e.g electrons have a wavelength (electron microscope!)


The Uncertainty Principle

Werner Heisenberg (1901-1976)and Niels Bohr


The Uncertainty Principle

It is impossible to know both the exact position and the exact momentum of a subatomic particle

4h

mx v

uncertainty in position, x

uncertainty in momentum, mv


Erwin Schrödinger (1887-1961)

Quantum Mechanics and Atomic Orbitals



• Schrödinger proposed wave mechanical model of the atom

• Electrons are described by a wave function, ψ

• The square of the wave function, ψ2, provides information onthe location of an electron (probability density or electron density)



• the denser the stippling, thehigher the probability of findingthe electron

• shape of electron densityregions depends on energy ofelectron


or

n = 1

n = 1

orbit

orbitalz

x

y

Bohr’s model:

Schrödinger’s model:

electron circles around nucleus

electron is somewherewithin that spherical region


Bohr’s model:


• requires only a single quantum number (n) to describe an orbit

• requires three quantum numbers (n, l, and m) to describe an orbital

n: principal quantum numberl : second or azimuthal quantum numberml: magnetic quantum number


(1) n = principal quantum number (analogous to Bohr model)

- the higher n, the higher the energy of the electron

- energy of electron in a given orbital:

2

1n

RchE H


- is always a positive integer: 1, 2, 3, 4 ….


(2) l = azimuthal quantum number


- takes integral values from 0 to n-1 n = 3e.g.

- l is normally listed as a letter:

Value of l: 0 1 2 3letter: s p d f

- l defines the shape of an electron orbital



z

x

y

s-orbital p-orbital(1 of 3)

d-orbital(1 of 5)

f-orbital(1 of 7)


(3) ml = magnetic quantum number


- takes integral values from -l to +l, including 0

l = 2e.g.

- ml describes the orientation of an electron orbital in space


Shells:

• are sets of orbitals with the same quantum number, n

Subshells:

• are orbitals of one type within the same shell

• a shell of quantum number n has n subshells

• total number of orbitals in a shell is n2

4f subshell

n=3 shell


n = 1 2 43

l = 0 0, 1 0, 1, 2 0, 1, 2, 3

1s 2s, 2p 3s, 3p, 3d 4s, 4p, 4d, 4f

ml = 0 0, -1,0,1 0; -1,0,1; -2,-1,0,1,2 0; -1,0,1; -2,-1,0,1,2; -3,-2,-1,0,1,2,3

# orbitalsin subshell

1 1 3 1 3 5 1 3 5 7

Total # of orbitalsin shell

1 4 9 16


1st floor

2nd floor

3rd floor

standard-room

2s-room

3s-room

2promotion-room

3p-room 3deluxe-room


Orbital energy levelsin the Hydrogen Atom


What is the designation for the n=3, l=2 subshell ?

What are the possible values for ml for each of these orbitals ?

How many orbitals are in this subshell ?


Which of the following combinations of quantum numbersis possible?

n=1, l=1, ml= -1

n=3, l=2, ml= 1

n=2, l=1, ml= -2

n=3, l=0, ml= -1


Representation of Orbitals

1s 2s 3s



2p orbitals



all three p orbitals



3d orbitals


Which combination of quantum numbers is possible for theorbital shown below?

(a) n=1, l=0, ml= 0

(b) n=2, l=-1, ml= 1

(c) n=3, l=3, ml= -2

(d) n=3, l=2, ml= -1


There is a fourth quantum number that characterizes electrons:

spin magnetic quantum number, ms

ms can only take two values, +1/2 or -1/2


Wolfgang Pauli (1900-1958) A. Einstein & W. Pauli


Pauli’s Exclusion Principle:

No two electrons in an atom can have the same set of 4 quantum numbers, n, l, ml, and ms

For a given orbital, e.g. 2s, n, l, ml are fixed:

n=2, l=0, ml =0

=> an orbital can only contain two electron if they differ in ms


2s 2p

A maximum of 2 electron can occupy one orbital, IF these two electrons have opposite spin:

n=2, l=0, ml =0, ms = +1/2n=2, l=0, ml =0, ms = -1/2

arrows pointing up/down indicate electron spin


Energy levels in the hydrogen atom:

all subshells of a given shellhave the same energy


Energy levels in many-electron atoms:

• In many-electron atoms, the energy of an orbital increases with l, for a given n

• In many-electron atoms, the lower energy orbitals get filled first

• orbitals with the same energy are said to be

degenerate


Electron Configurations:

1H 1s1

2He

3Li

4Be

6C

7N

10Ne

11Na

1s2

1s22s1

1s22s2

1s22s22p2

1s22s22p3

1s22s22p6

1s22s22p63s1

Line Notation:


7N 1s22s22p3

Hund’s Rule:

For degenerate orbitals, the energy is minimized when the number of electrons with the same spin is maximized

Electron Configurations:

=> degenerate orbitals (p, d, etc)get filled with one electron each first (same spin).


the Aufbau Principle helps you to remember the order in which orbitals get filled:

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d 6f

7s 7p 7d 7f

[Ne]


14Si 1s22s22p63s23p2 Line notation

orbital diagram(no energy info)

s

p

d

1

2

3

Condensed line notation

“core electrons”

3s23p2

“valence (outer shell) electrons”

1s22s22p63s23p2

[Ne]


14Si Line notation

orbital diagram(no energy info)

s

p

d

1

2

3

Condensed line notation3s23p2

Valence electrons take part in bonding


What is the electronic structure of Cl?

s

p

d

1

2

3

valence electrons (7)

17Cl :

core electrons =

electron configurationof the preceding noble gas

3s23p5[Ne]


core electrons =



What is the electronic structure of Ca?

s

p

d

1

2

3

20Cl : 4s2

4

f

(4s orbital is filled before 3d !)[Ar]


core electrons =



What is the electronic structure of Br?

s

p

d

1

2

3

35Br : 3d104s24p5

4

f

(4s orbital is filled before 3d !)[Ar]

For main group elements,electrons in a filled d-shell(or f-shell) are not valenceelectrons


Does it matter in which order the electron configuration is written ?

s

p

d

1

2

3

35Br : 1s22s22p63s23p63d104s24p5

4

f

1s22s22p63s23p64s23d104p5or:

ordered by orbital number

ordered by energy

NO, both are correct!


s

p

d

1

2

3

4

f

What is the electron configuration of vanadium (V)?

23V: [Ar] 3d34s2

core electrons =



(4s orbital is filled before 3d !)


s

p

d

1

2

3

4

f

What is the electron configuration of chromium (Cr)?

24Cr: [Ar] 3d54s1

[Ar] 3d44s2 is less stable than [Ar] 3d54s1

A half-filled or completely filled d-shell is a preferred configuration


1s

2s 2p

3s 3p

4s

3d

4p

4f


What is the electronic structure of the Ca ion?

s

p

d

1

2

3

20Ca : 4s2

4

f

[Ar]

20Ca2+ : [Ar]


● Atoms tend to gain or lose the number of electrons

needed to achieve the

electron configuration of the closest noble gas

● Metals tend to lose electrons to form cations

● Nonmetals tend to gain electrons to form anions


What is the electronic structure of the ion formed by Se?

s

p

d

1

2

3

34Se : 3d104s24p4

4

f

[Ar]

34Se2- : [Ar] 3d104s24p6 = [Kr]


What is the electronic structure of the ion formed by Br?

s

p

d

1

2

3

35Br : 3d104s24p5

4

f

[Ar]

35Br- : [Ar] 3d104s24p6 = [Kr]


What is the electronic structure of the ion formed by Rb?

s

p

d

1

2

3

37Rb : 5s1

4

f

[Kr]

37Rb+ : [Kr]

5


37Rb+ :

35Br- : [Ar] 3d104s24p6 = [Kr]

34Se2- : [Ar] 3d104s24p6 = [Kr]

[Ar] 3d104s24p6 = [Kr]

37Rb+35Br-

34Se2- , , , and 36Kr have the same electron configuration:

they are isoelectronic


a.

b.

c.

d.

Which of the four orbital diagrams written below for nitrogen violates the Pauli Exclusion Principle?

violates Hund’s rule(all spins must point in the same direction)

violates Hund’s rule(degenerate orbitals get one electron each, first)

doesn’t violate anything

violates Pauli’s Exclusion Principlethere are two same spin electrons in one orbital, i.e. all 4 quantum numbers are the

same – which is impossible1s 2s 2p


What is the total number of orbitals in the fourth shell (n=4) ?

a. 16 b. 12 c. 4 d. 3

n=4

l = 0 1 2 3s p d f

ml = 0 -1,0,1 -2,-1,0,1,2 -3,-2,-1,0,1,2,3

one s + three p + five d + 7 f orbitals

=16 orbitals

what is the total number of different s,p, d and f orbitals?

(n2)


What is the number of subshells in the third shell (n=3) ?

a. 18 b. 9 c. 3 d. 1

n=3

l = 0 1 2s p d

How many different types of orbitals are there?


What is the electron configuration of the sodium cation, Na+ ?

a. 1s22s22p63s1 b. 1s22s22p6

c. 1s22s22p63s2 d. 1s22s22p7

11Na+ = 11 electrons -1 = 10 electrons

1s2 2s2 2p6

chapter 6: electronic structure of atoms light is a form of electromagnetic radiation (emr): an...

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