copyright©2000 by houghton mifflin company. all rights reserved. 1 atomic structure and periodicity...

Copyright©2000 by Houghton Mifflin Company. All rights reserved.

1

Atomic Structure and Periodicity

Chapter 7


2

Overview

Introduce Electromagnetic Radiation and The Nature of Matter.

Discuss the atomic spectrum of hydrogen and Bohr model.

Describe the quantum mechanical model of the atoms and quantum numbers.

Use Aufbau principle to determine the electron configuration of elements.

Highlight periodic table trends.


3

Matter and Energy

Matter and Energy were two distinct concepts in the 19th century.

Matter was thought to consist of particles, and had mass and position.

Energy in the form of light was thought to be wave-like.


4

Physical Properties of Waves

Wavelength () 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.


5

Properties of Waves

Frequency () is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s).

The speed (v or c) of the wave = x


6

Electromagnetic Radiation

Electromagnetic radiation travels through space at the speed of light in a vacuum.

Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves.


7

Maxwell (1873), proposed that visible light consists of electromagnetic waves.

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

All electromagnetic radiation x c

7.1


8

Electromagnetic Waves

Electromagnetic Waves have 3 primary characteristics:

1. Wavelength: distance between two peaks in a wave.

2. Frequency: number of waves per second that pass a given point in space.

3. Speed: speed of light is 2.9979 108 m/s.


9

Wavelength and frequency can be interconverted.

= c/

(neu)= frequency (s1)

(lamda) = wavelength (m)

c = speed of light (m s1)


10

Electromagnetic Spectrum


11

Planck’s Constant

E = change in energy, in Jh = Planck’s constant, 6.626 1034 J s = frequency, in s1

= wavelength, in mn = integer = 1,2,3…

Transfer of energy is Transfer of energy is quantizedquantized, and can only , and can only occur in discrete units, called occur in discrete units, called quantaquanta..

E hhc

= =

n n


12

Diffraction

X-Ray Diffraction showed also that light has particle properties.


13

Figure-7.5:

(a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of sodium chloride. The large spot in the center is from the main incident beam of X rays. (b) Bright spots in the diffraction pattern result from constructive interference of waves. The waves are in phase; that is, their peaks match. (c) Dark areas result from destructive interference of waves. The waves are out of phase; the peaks of one wave coincide with the troughs of another wave.


14

Energy and Mass

Energy has mass

E = mc2 Einstein’s Equation

E = energy

m = mass

c = speed of light


15

Energy and Mass

Ehc

photon =

mhcphoton =

Radiation in itself is quantized


16

Wavelength and Mass

= wavelength, in m

h = Planck’s constant, 6.626 1034 J s = kg m2 s1

m = mass, in kg

v = speed, in ms1

= h

m

de Broglie’s Equationde Broglie’s Equation


17

x = c = c/ = 3.00 x 108 m/s / 6.0 x 104 Hz = 5.0 x 103 m

Radio wave

A photon has a frequency of 6.0 x 104 Hz. Convertthis frequency into wavelength (nm). Does this frequencyfall in the visible region?

= 5.0 x 1012 nm


18

Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths.

Atomic Spectrum of Hydrogen


19

Atomic Spectrum of Hydrogen

Continuous spectrum: Contains all the wavelengths of light.

Line (discrete) spectrum: Contains only some of the wavelengths of light.


20

1. e- can only have specific (quantized) energy values

2. light is emitted as e- moves from one energy level to a lower energy level

Bohr’s Model of the Atom (1913)

En = -RH ( )z2

n2

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

RH (Rydberg constant) = 2.18 x 10-18J

7.3


21

E = h

E = h


22

Ephoton = E = Ef - Ei

Ef = -RH ( )1n2

f

Ei = -RH ( )1n2

i

i fE = RH( )

1n2

1n2

nf = 1

ni = 2

nf = 1

ni = 3

nf = 2

ni = 3


23

= h/mv

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

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

What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?

m in kgh in J•s u in (m/s)


24

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

Ephoton = E = -1.55 x 10-19 J

= 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J

= 1280 nm

Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state.

Ephoton = h x c /

= h x c / Ephoton

i fE = RH( )

1n2

1n2

Ephoton =

Ignore the (-) sign for

and


25

The Bohr ModelGround State: The lowest possible energy state for an atom (n = 1).

Ionization: nf = => 1/nf2 = 0 =>

E=0 for free electron.Any bound electron has a negative value to this reference state.


26

E = h =

hc

P = mv

To be well memorized

E = mc2

i fE = RH( )

1n2

1n2

Ephoton =


27

Schrödinger Wave Equation

In 1926 Schrödinger wrote an equation that described both the particle and wave nature of the e-

Wave function () describes:

1. energy of e- with a given

2. probability of finding e- in a volume of space

Schrödinger's equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.


28

Quantum Mechanics

Based on the wave properties of the atom

= wave function

= mathematical operator

E = total energy of the atom

A specific wave function is often called an orbital.

H E =

H


29


fn(n, l, ml, ms)

principal quantum number n

n = 1, 2, 3, 4, ….

n=1 n=2 n=3

distance of e- from the nucleus


30

Probability Distribution

SQUARE of the wave function:

probability of finding an electron at a given position

Radial probability distribution is the probability distribution in each spherical shell.


31

e- density (1s orbital) falls off rapidly as distance from nucleus increases

Where 90% of thee- density is foundfor the 1s orbital


32

Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution.


33

Heisenberg Uncertainty Principle

x mvh

4

x = position

mv = momentum

h = Planck’s constant

The more accurately we know a particle’s position, the less accurately we can know its momentum.


34

Quantum Numbers (QN)

1. Principal QN (n = 1, 2, 3, . . .) - related to size and energy of the orbital.

2. Angular Momentum QN (l = 0 to n 1) - relates to shape of the orbital.

3. Magnetic QN (ml = l to l) - relates to orientation of the orbital in space relative to other orbitals.

4. Electron Spin QN (ms = +1/2, 1/2) - relates to the spin states of the electrons.


35

= fn(n, l, ml, ms)

angular momentum quantum number l

for a given value of n, l = 0, 1, 2, 3, … n-1

n = 1, l = 0n = 2, l = 0 or 1

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

Shape of the “volume” of space that the e- occupies

l = 0 s orbitall = 1 p orbitall = 2 d orbitall = 3 f orbital



36

ml -l to +l


37

Each orbital can take a maximum of two electrons and a minimum of Zero electrons.

Zero electrons does not mean that the orbital does not exist.


38

Degenerate


39

Pauli Exclusion Principle

In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms).

Therefore, an orbital can hold only two electrons, and they must have opposite spins.


40

Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.


41

Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p

orbital. (b) The boundary surface representations of all three 2p orbitals.


42

ml = -1 ml = 0 ml = 1

2p

Degenerate Orbitals


43

Figure 7.16: Representation of the 3d orbitals.


44

ml = -2 ml = -1 ml = 0 ml = 1 ml = 2

3d


45

How many 2p orbitals are there in an atom?

2p

n=2

l = 1

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

3 orbitals

How many electrons can be placed in the 3d subshell?

3d

n=3

l = 2

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

5 orbitals which can hold a total of 10 e-


46

Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals.

Probability to bein the nucleus

Zero probability to bein the nucleus

P orbital is more diffuse


47

Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p, and 3d orbitals.


48

Energy of orbitals in a single electron atom

Energy only depends on principal quantum number n

En = -RH ( )1n2

n=1

n=2

n=3


49

Energy of orbitals in a multi-electron atom

Energy depends on n and l

n=1 l = 0

n=2 l = 0n=2 l = 1

n=3 l = 0n=3 l = 1

n=3 l = 2


50

“Fill up” electrons in lowest energy orbitals (Aufbau principle)

H 1 electron

H 1s1

He 2 electrons

He 1s2

Li 3 electrons

Li 1s22s1

Be 4 electrons

Be 1s22s2

B 5 electrons

B 1s22s22p1

C 6 electrons

? ?


51

Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.


52

C 6 electrons

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

C 1s22s22p2

N 7 electrons

N 1s22s22p3

O 8 electrons

O 1s22s22p4

F 9 electronsF 1s22s22p5

Ne 10 electronsNe 1s22s22p6


53

Order of orbitals (filling) in multi-electron atom

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s


54

Figure 7.26: Electron configurations for potassium through krypton.


55

Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.


56

What is the electron configuration of Mg?

Mg 12 electrons

1s < 2s < 2p < 3s < 3p < 4s

1s22s22p63s2 2 + 2 + 6 + 2 = 12 electrons

7.7

Abbreviated as [Ne]3s2 [Ne] 1s22s22p6

What are the possible quantum numbers for the last (outermost) electron in Cl?

Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s

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


57

Valence Electrons

Atom Valence Electrons

Ca 2

N 5

Br 7

The electrons in the outermost principle The electrons in the outermost principle quantum level of an atom.quantum level of an atom.

Inner electronsInner electrons are called are called corecore electrons. electrons.


58

Broad Periodic Table Classifications

Representative Elements (main group): filling s and p orbitals (Na, Al, Ne, O)

Transition Elements: filling d orbitals (Fe, Co, Ni)

Lanthanide and Actinide Series (inner transition elements): filling 4f and 5f orbitals (Eu, Am, Es)


59

Figure 7.36: Special names for groups in the periodic table.


60

Ionization Energy

The quantity of energy required to remove an electron from the gaseous atom or ion.

This is an Endothermic Process: Energy is absorbed & Sign will be +ve


61

I1 + X (g) X+

(g) + e-

I2 + X+ (g) X2+(g) + e-

I3 + X2+ (g) X3+(g) + e-

I1 first ionization energy

I2 second ionization energy

I3 third ionization energy

I1 < I2 < I3


62


63


64

Figure 7.31: The values of first ionization energy for the elements

in the first six periods.


65

Exceptions

Be 1s2 2s2

B 1s22s22p1 Shielded Electron

N 1s22s2sp3

O 1s22s22p4

Repulsion to doubly electrons


66

Periodic Trends

First ionization energy:

increases from left to right across a period;

decreases going down a group.


67

General Trend in First Ionization Energies

Increasing First Ionization Energy

Incr

ea

sing

Firs

t Io

niz

atio

n E

ner

gy


68

Electron Affinity

The energy change associated with the addition of an electron to a gaseous atom.

X(g) + e X(g)

This is an Exothermic Process: Energy is Released & Sign will be -ve


69

X (g) + e- X-(g)

F (g) + e- X-(g)

O (g) + e- O-(g)

H = -328 kJ/mol EA = +328 kJ/mol

H = -141 kJ/mol EA = +141 kJ/mol


70

Figure 7.33: The electron affinity values for atoms among the first 20 elements that form

stable, isolated X- ions.


71


72

Exceptions

C-(g) can be formed easily while N-

(g) cannot be formed easily:

C- 1s22s2p3

N- 1s22s22p4

O-(g) can be formed because the larger

positive nucleus overcome pairing repulsions.

Extra repulsion


73

Periodic Trends

Atomic Radii:

decrease going from left to right across a period;

increase going down a group.


74

Figure 7.35: Atomic radii (in picometers) for selected atoms.


75

Information Contained in the Periodic Table

1. Each group member has the same valence electron configuration (these electrons primarily determine an atom’s chemistry).

2. The electron configuration of any representative element.

3. Certain groups have special names (alkali metals, halogens, etc).

4. Metals and nonmetals are characterized by their chemical and physical properties.


76

Paramagnetic

unpaired electrons

2p

Diamagnetic

all electrons paired

2p

copyright©2000 by houghton mifflin company. all rights reserved. 1 atomic structure and periodicity...

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