principles of chemistry i chem 1211 chapter 7 dr. augustine ofori agyeman assistant professor of...

PRINCIPLES OF CHEMISTRY I

CHEM 1211

CHAPTER 7

DR. AUGUSTINE OFORI AGYEMANAssistant professor of chemistryDepartment of natural sciences

Clayton state university

CHAPTER 7

ELECTRONIC STRUCTURE OF ATOMS

ELECTROMAGNETIC RADIATION

- Also known as radiant heat or radiant energy

- One of the ways by which energy travels through space

- Consists of electric and magnetic fields which are perpendicularto each other and to the direction of propagation

Examples

heat energy in microwaveslight from the sun

X-ray radio waves

- Light properties is a key concept for understandingelectronic structure

- Studies of atomic structure has come from observations of the interaction of visible light and matter

- To study the properties of electrons in atoms, it is helpful to understand waves and electromagnetic radiation


Three Characteristics of Waves

Wavelength (λ) - Distance for a wave to go through a complete cycle

(distance between two consecutive peaks or troughs in a wave)

Frequency (ν)- The number of waves (cycles) per second that pass

a given point in space

Speed (c)- All waves travel at the speed of light in vacuum (3.00 x 108 m/s)


one second

λ1

λ3

λ2

ν1 = 4 cycles/second



amplitude

peak

trough


node

- Inverse relationship between wavelength and frequency

λ α 1/ν

c = λ ν = 3.00 x 108 m/s

λ = wavelength (m)

ν = frequency (cycles/second = 1/s = s-1 = hertz = Hz)

c = speed of light (3.00 x 108 m/s)


Gamma rays

X rays Ultr-violet

Infrared Microwaves Radio frequency FM Shortwave AM

Vis

ible

Visible Light: VIBGYORViolet, Indigo, Blue, Green, Yellow, Orange, Red

400 – 750 nm

- White light is a blend of all visible wavelengths

- Can be separated using a prism

Wavelength (m)

Frequency (s-1)

10-11 103

1020104


An FM radio station broadcasts at 90.1 MHz. Calculate the wavelength (in m, nm, Ǻ) of the corresponding radio waves

c = λ ν

λ = ?ν = 90.1 MHz = 90.1 x 106 Hz = 9.01 x 107 Hz

c = 3.00 x 108 m/s

λ = c/ ν = [3.00 x 108 m/s]/[9.01 x 107 Hz]

= 3.33 m = 3.33 x 109 nm = 3.33 x 1010 Ǻ


Max Planck’s Postulate

- Energy can be gained or lost by whole-number multiples

- Change in energy (E) = nhν

n = an integer (1, 2, 3, …..)

h = Planck’s constant (6.626 x 10-34 joule-second, J-s)

ν = frequency of electromagnetic radiation absorbed or emitted

QUANTIZATION OF ENERGY

Max Planck’s Postulate

- Energy is quantized and can occur only in discrete units of size, hν

- Matter is allowed to emit or absorb energy only in whole-number multiples

- Each of these small quantities (packets) of energy is the quantum

- Many scientists dismissed Planck’s idea


Albert Einstein’s Proposal

- Electromagnetic radiation is itself quantized

- Electromagnetic radiation can be viewed as a stream of‘tiny particles’ called photons

h = Planck’s constant (6.626 x 10-34 joule-second, J-s)ν = frequency of the radiation

λ = wavelength of the radiation


λ

hchνEphoton

Photoelectric Effect

- A phenomenon in which electrons are emitted from the surface of a solid metal when light strikes

Eo = hνo

Eo = minimum energy required to remove an electron

νo = threshold frequency below which electrons are not emitted

by a given metal



Below νo - No electrons are emitted irrespective of the light intensity

Above νo - Number of electrons emitted increases with light intensity

- Kinetic energy increases linearly with frequency


o2

)k(electron hνhνmv2

1E

m = mass of electron (kg)

v = velocity of electron (m/s)

hν = energy of incident electron (J)

hνo = energy required to remove electron from metal’s surface (J)



E = mc2

E = energy

m = mass

c = speed of light

Einstein’s Equation


λc

h

c

hc/λ

c

Em

22

The Dual Nature of Light- Electromagnetic radiation exhibits wave properties and

particulate properties

Einstein’s Equation


λv

h

λc

hm

mv

hλ

For a particle with velocity, v

- Particles have wavelength associated with them- Wavelength is inversely proportional to mass

- In conclusion, matter and energy are not distinct

De Broglie’s Equation


mv

hλ

Calculate the wavelength of an electron of mass 8.81 x 10-31 kg,traveling at a speed of 1.5 x 107 m/s

λ = ? v = 1.5 x 107 m/s m = 8.81 x 10-31 kg

λ = (6.626 x 10-34 j-s)/[(8.81 x 10-31 kg)(1.5 x 107 m/s)]

= 5.0 x 10-11 m

De Broglie’s Equation


THE ATOMIC SPECTRUM

SpectrumIntensity of light as a function of wavelength

Transmission- Electromagnetic radiation (EM) passes through matter

without interaction

Absorption- An atom (or ion or molecule) absorbs EM and

moves to a higher energy state (excited)

Emission- An atom (or ion or molecule) releases energy and

moves to a lower energy state

THE ATOMIC SPECTRUM

- The excited atoms release energy by emitting light

- The emitted light has various wavelengths called emission spectrum

- The emission spectrum of an atom is called line spectrum

- Lines corresponding to discrete wavelengths are seen when passed through a prism

- Implies electron energy levels are quantized

- The emission spectrum of the sun (white light) is a continuous spectrum when passed through a prism (ROYGBIV-rainbow)

RYDBERG EQUATION

- A study of the wavelengths from the line spectra of the hydrogen atom

22

21

H n

1

n

1R

λ

1

RH = Rydberg constant = 1.097 x 107 m-1

n1 and n2 are positive integers

n1 < n2

THE BOHR MODEL

- An electron in a hydrogen atom moves around the nucleus in certain allowed circular orbits

- Negatively charged electrons are attracted to the positively charged nucleus

- Electrons are charged particles under acceleration and hence radiate energy (emit light and lose energy)

2

218

n

ZJ10x2.178E

n = integer (the larger the n value, the larger the orbital radius)Z = nuclear charge (Z = 1 for hydrogen, one photon)

- If n is infinitely large (n = ∞), E = 0

As the electron gets closer to the nucleus- E becomes more negative

- Energy is released from the system

THE BOHR MODEL

- Energy required to excite the H electron from one level to another level

(Z = 1)

E = Efinal – Einitial

= energy level n2 – energy level n1

21

22

18

n

1

n

1J10x2.178E

THE BOHR MODEL

Limitations

- Bohr’s model does not work for any other atoms apart from H

- Electrons do not move in circular orbits around the nucleus

THE BOHR MODEL

Calculate the energy required to excite the hydrogen electronfrom level n = 1 to level n = 3. Calculate the wavelength oflight that must be absorbed by a H atom in its ground state

to reach its excited state

THE BOHR MODEL

21

22

18

n

1

n

1J10x2.178E

J10x1.9361

1

3

1J10x2.178ΔE 18

2218

m10x1.03J)10x(1.936

m/s)10xs)(3.00J10x(6.626

ΔE

hcλ 7

18

834

THE BOHR MODEL

QUANTUM MECHANICS

- Developed by Heisenberg, de Broglie, and Schrödinger

- An electron bound to a nucleus seems to be a standing wave (stationary waves such as those from guitar strings)

QUANTUM MECHANICS

Schrödinger’s Equation

Ĥψ = Eψ

ψ = wave function (coordinates x, y, z function)

ψ2 = probability of finding an electron at a given point in space

Ĥ = operator

E = total energy of atom (sum of potential and kinetic energies)

THE WAVE FUNCTION

- A specific wave function is called the orbital

- It is difficult to know precisely the pathway (position and momentum) of an electron in a given time

THE WAVE FUNCTION

Heisenberg Uncertainty Principle

4π

hΔ(mv)Δx

x = uncertainty in a particle’s position

(mv) = uncertainty in a particle’s momentum

Momentum = product of mass and velocity of an object

QUANTUM NUMBERS

- Describes various properties of the orbital

Principal Quantum Number (n)- Called the electron shell

- Related to the size and energy of the atomic orbital- Has integral values 1, 2, 3, ……

- Orbital becomes larger as n increases (electron is farther from the nucleus)

- Electron energy increases with increasing n (electron is less tightly bound and energy is less negative)- Orbitals with the same energy (same n value) are said to

be degenerate


Angular Momentum (Azimuthal) Quantum Number (l)- Called electron subshell

- Related to the shape of the atomic orbitals- Has integral values 0, 1, 2, 3, ……, n-1 (for each value of n)

- The values of l are assigned letters

Value of l 0 1 2 3 4

Letter used s p d f g

QUANTUM NUMBERS


Magnetic Quantum Number (ml)- Related to the orientation of the orbital in space relative to

the other orbitals in the atom- Has integral values between l and –l, including 0 (ml = 2l + 1)

Value of l 0 1 2 3 4

Letter used s p d f g

# of orbitals (ml) 1 3 5 7 9

QUANTUM NUMBERS


Electron Spin Quantum Number (ms)

- Can have only one of the two values +1/2 and -1/2

- Electrons can spin in one of two opposite directions

- Two electrons with the same spin are parallel

- Two electrons with different spins are paired(one +1/2 and the other -1/2)

QUANTUM NUMBERS

Shell 1 1 subshell 1s 2 electrons

Shell 2 2 subshells

3 subshells

4 subshells

Shell 3

Shell 4

2s2p

2 electrons6 electrons10 electrons14 electrons

2 electrons 6 electrons2 electrons6 electrons10 electrons

3s3p3d

4s4p4d4f

- The value of n and the letter for l are used to designate orbitals

n l

0

01

012

0123

Orbitaldesignation

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

# of subshells

# ofelectrons

QUANTUM NUMBERS

For shell n

- The number of orbitals = n2

- The maximum number of electrons = 2n2

QUANTUM NUMBERS

n

1

2

3

4

Subshell

s

s, p

s, p, d

s, p, d, f

Number of orbitals

1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

Maximum numberof electrons

2

8

18

32

QUANTUM NUMBERS

PAULI EXCLUSION PRINCIPLE

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

- Electrons in the same orbital has the same n, l, and ml

- These electrons should have different values of ms

- Implies an orbital can hold a maximum of two electrons

- The two electrons in any orbital must have opposite spins

ORBITAL SHAPES AND ENERGIES

- An orbital is a region of space within an electron subshell

- The electron with a specific energy has a high probability of being found

- An orbital can accommodate a maximum of 2 electrons

- The orbitals contain areas of high probability separated by areas of low probability

- The areas of low probability are called nodes

The s orbital

- The number of nodes for s orbitals = n-1

- The s orbital is spherical

- Its function always has a positive sign


The p orbital

- Note that there are no 1p orbitals

- p orbitals have 2 lobes separated by a node at the nucleus

- Labeled according to the xyz cordinate axis system 2p orbital with lobes centered along the x-axis is 2px orbital 2p orbital with lobes centered along the y-axis is 2py orbital 2p orbital with lobes centered along the z-axis is 2pz orbital

- The p orbital has positive and negative signs (phases)

- Size of lobes increase with increasing n


The d orbital

- Note that there are no 1d nor 2d orbitals

- The d orbitals have two different fundamental shapes

- dxy, dxz, dyz, dx2-y2: four lobes centered in the indicated planes- dz2: two lobes along the z axis and a belt centered in the xy plane

- Size of lobes increase with increasing n


The f orbital

- Note that there are no 1f, 2f, nor 3f orbitals

- Shapes are more complex than the d orbitals


POLYELECTRONIC ATOMS

- Atoms with more than one electron

Three energy contributions- The kinetic energy of the electrons as they move around the

nucleus- The potenital energy of attraction between the nucleus and the

electrons- The potenital energy of repulsion between the electrons

- Electron repulsion cannot be calculated exactly since electron pathways are not exactly known (electron correlation problem)

- Orbitals in a given principal quantum level for H atoms are degenerate

- No orbitals are degenerate in polyelectronic atoms

- Order of increasing energy levels s < p < d < f

POLYELECTRONIC ATOMS

ELECTRON CONFIGURATION

- Elements in the periodic table are arranged in order of increasing atomic number (number of protons)

- Similar to protons, electrons are added one by one to the nucleus to build up elements (Aufbau Principle)

Rules for assigning electrons

- Electron subshells are filled in order of increasing energy (s, p, d, f)

- All orbitals of a subshell acquire single electrons before any orbital acquire a second electron (Hund’s rule)

- All electrons in singly occupied orbitals must have the same spin

- A maximum of 2 electrons can exist in a given orbital and must have opposite spins (Pauli principle)


- Ordering of electron subshells is often complicated due to overlapsFor instance, the 3d subshell has higher energy than the 4s subshell

- Use of mnemonic for subshell filling is essential

1s

2s 2p

3s 3p 3d

4s

5s

4p 4d 4f

5p 5d 5f

6s

7s

6p 6d

7p

The (n+1)s orbitals alwaysfill before the nd orbitals


- Subshells containing electrons are designated using the sunshell numbers and letters (types)

- The number of electrons in a given subshell is indicated by a superscript

Carbon has 6 electrons: 1s22s22p2

Nitrogen has 7 electrons: 1s22s22p3

Sodium has 11 electrons: 1s22s22p63s1


ORBITAL DIAGRAMS

Hydrogen has electronic configuration written as 1s1

The orbital diagram is

H:

1s

Helium has electronic configuration written as 1s2

The orbital diagram is1s

He:

Lithium has electronic configuration written as 1s22s1

The orbital diagram is Li:1s

Boron has electronic configuration written as 1s22s22p1


B:

Beryllium has electronic configuration written as 1s22s2


2s

2s1s

2p2s

Be:

ORBITAL DIAGRAMS

Carbon has electronic configuration written as 1s22s22p2

The orbital diagram is C:

1s

Sodium has electronic configuration written as 1s22s22p63s1


Na:

Nitrogen has electronic configuration written as 1s22s22p3


2p2s

2s1s 2p

2p2s 3s

N:

ORBITAL DIAGRAMS

Neon has electronic configuration written as 1s22s22p6

The orbital diagram is Ne:

1s 2p2s

The electron configuration for sodium (Na) can be abbreviated as

[Ne]3s1

Magnesium (Mg) is abbreviated as [Ne]3s2

ABBREVIATED ELECTRON CONFIGURATION

Chromium (Cr) is expected to be [Ar]4s23d4

But is [Ar]4s13d5

Copper (Cu) is expected to be [Ar]4s23d9

But is [Ar]4s13d10

Tungsten (W) is expected to be [Xe]6s24f145d4

But is [Xe]6s14f145d5

Gold (Au) is expected to be [Xe]6s24f145d9

But is [Xe]6s14f145d10

ANOMALOUS ELECTRON CONFIGURATION

principles of chemistry i chem 1211 chapter 7 dr. augustine ofori agyeman assistant professor of...

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