Atomic StructureAtomic Structure

Chapter 7:

1. Describe the properties of electromagnetic radiation.

2. Understand the origin of light from excited atoms and its relationship to atomic structure.

3. Describe the experimental evidence for wave-particle duality.

4. Describe the basic ideas of quantum mechanics.

5. Define the three quantum numbers and their relationship to atomic structure.

Electromagnetic RadiationElectromagnetic Radiation

• Radiation is Radiation is __________________________!!• List forms of electromagnetic radiation:List forms of electromagnetic radiation:

____________________________________________________

____________________________________________________• Maxwell TheoryMaxwell Theory (1831-1879): describe (1831-1879): describe

all forms of radiation in terms of ________all forms of radiation in terms of ________

________________________________.________________________________.• Einstein TheoryEinstein Theory (1879-1955): light has (1879-1955): light has

______________________________________________________________..

Wave PropertiesWave Propertieswavelength

Visible light

Ultraviolet radiation

Electromagnetic RadiationElectromagnetic Radiation

Frequency – hertz (s-1)Speed = wavelength (m) x frequency (s-1)

c = x v

What is the frequency of orange light, What is the frequency of orange light, which has a wavelength of 625 nm?which has a wavelength of 625 nm?

Students should be familiar with conversion of units and conversion between and v.

The Visible Spectrum of LightThe Visible Spectrum of Light

• Long wavelengthLong wavelength --> ______ frequency --> ______ frequency

_____ _____ energyenergy• Short wavelengthShort wavelength --> _____ frequency --> _____ frequency

_____ energy

EnergyEnergy and and FrequencyFrequency

• Max PlanckMax Planck (1858-1947): the (1858-1947): the energy of a vibrating systems is energy of a vibrating systems is proportionalproportional to the frequency of to the frequency of vibration.vibration.

• The proportionality constantThe proportionality constanthh = Planck’s constant = Planck’s constant = 6.6260693 x 10= 6.6260693 x 10-34-34 J s J s

E = h v

Radiation given off by a Heated Radiation given off by a Heated BodyBody

• Planck solved the “___________________”.

• Vibrations are _________ – only vibrations with specific frequencies are allowed.

• There is a distribution of vibrations in a object.

Quantization of EnergyQuantization of Energy

• An object can gain or lose energy by An object can gain or lose energy by absorbing or emitting radiant energy in absorbing or emitting radiant energy in QUANTAQUANTA..

• Energy of radiation is proportional to Energy of radiation is proportional to frequency.frequency.

Light with large Light with large (small (small vv) has a _____ E.) has a _____ E. Light with a short Light with a short (large (large vv) has a ____ ) has a ____

E.E.

E = h v

Photoelectric EffectPhotoelectric Effect

• Experiment demonstrates the _______ _____________________________.

No e- observed until light of a certain minimum E is used.

Photoelectric EffectPhotoelectric Effect• Classical theory said that E of ejectedClassical theory said that E of ejected

electron should increase with increaseelectron should increase with increasein light frequency—not observed!in light frequency—not observed!

• No eNo e-- observed until light of a certain observed until light of a certainminimum E is used.minimum E is used.

• If the frequency is above the minimum,If the frequency is above the minimum,the number of ethe number of e-- ejected depends on ejected depends onlight intensity.light intensity.

• Einstein explained the photoelectric Einstein explained the photoelectric effect: light consists of “__________” effect: light consists of “__________” particles called particles called PHOTONS – PHOTONS – _______________._______________.

• The energy of each photon is proportional to the ______________of radiation (Planck’s relation).

• The greater the intensity of light, the more photons are available to strike per unit of time.

Show that the energy of a mol of Show that the energy of a mol of blue blue photons (photons ( = = 400 nm) is higher than the energy of a mol of 400 nm) is higher than the energy of a mol of red red

photons (photons (=685 nm)=685 nm)

Using Planck’s EquationUsing Planck’s Equation

• As frequency (v) increases, energy (E) __________.• As wavelength () decreases, energy (E)

_________.

v = c/ E = h v

E = h v = h c

Students should be familiar with frequency, wavelength, and energy

calculations.

= h c v~

(wavenumber)

What is the color of light when its What is the color of light when its frequency is 6.0 x 10frequency is 6.0 x 101414 s s-1-1??

PhotosynthesisPhotosynthesis

• Chlorophylls absorb blue and red light and carotenoids absorb blue-green light, but green and yellow light are not effectively absorbed by photosynthetic pigments in plants; therefore, light of these colors is either reflected by leaves or passes through the leaves. This is why plants are green.

Spectrum of White LightSpectrum of White Light

Spectrum of Excited Hydrogen GasSpectrum of Excited Hydrogen Gas

• Excited atoms emit light of only certain wavelengths. –Evidence of ____________________.

• Line Emission Spectra of Excited Atoms.Line Emission Spectra of Excited Atoms.• The wavelengths of emitted light depend on

______________________________.

Which Mathematical Expression represents Which Mathematical Expression represents the Regular Patterns of Emission?the Regular Patterns of Emission?

• Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919) developed an equation:

• Rydberg equation – to calculate the _________________

____________________________________.• Rydberg constant = R

R = 1.0974 x 107 m-1

1

= R ( )1

22

1

n2

when n > 2n = 3 , =red linen = 4 , l = green line,

Etc. Balmer Series

Atomic View of the Early 20Atomic View of the Early 20thth CenturyCentury

An electron (e-) An electron (e-) traveled about the traveled about the nucleus in an orbit.nucleus in an orbit.

1.1.Any orbit should be Any orbit should be possible and so is possible and so is any energy.any energy.

2.2.But a charged But a charged particle moving in an particle moving in an electric field should electric field should emit energy. emit energy.

End result should be End result should be matter self-matter self-destruction!destruction!

+Electronorbit

Bohr ModelBohr Model

• Niels Bohr (1885-1962) connected the observation of the spectra of excited atoms with the quantum ideas of Planck and Einstein.

• Based on Rutherford’s work – electrons are arranged in space outside the atom.

• Bohr model shows electrons moving in a circular orbit around the nucleus.

• Bohr postulated:1.- An electron could occupy only __________

___________or energy levels in which it is stable.

2.-The energy of the electron in the atom is ______________.

Atomic Spectra and BohrAtomic Spectra and Bohr

• n ___________ quantum number• n is a _________________ having values of 1, 2, 3

and so on.• The energy of attraction between oppositely

charged bodies (negative electron and positive nuclear proton) has a negative value. The value becomes more negative as the bodies move closer together (Coulomb’s law).

• As the value of n increases, the energy becomes less negative, the distance of the electron from the nucleus increases.

Potential energy of electron

in the nth level

= En = -R h c n 2

Atomic Spectra and BohrAtomic Spectra and Bohr

• Only orbits where n = integral number are permitted.If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra.

n = 1

n = 2E = -C (1/ 2 2 )

E = -C (1/1 2 )

Ground State and Excited StateGround State and Excited State

• Ground state: The state of an atom in which all electrons are in the ______________________.

• Excited state: The state of an atom in which at least one electron is ______________________ ____________________.

CC alculate CC alculate E for an e- of the H atom “falling” E for an e- of the H atom “falling” from high energy level (n = 2) to low energy from high energy level (n = 2) to low energy

level (n = 1). level (n = 1).

Atomic Spectra and BohrAtomic Spectra and Bohr

• The amount of energy that must be absorbed by the atom so that an electron can move from the first to the second energy state is 3/4RhC or 984 kJ/mol of atoms – no more or less – energy levels in the H atom are quantized – only certain amounts of energy may be absorbed or emitted.

• When an electron “falls” from a level of higher n to one of lower n, ________ energy. The negative sign indicates energy is _________, 984 kJ must be _______ per mole of H atoms.

• The energy ________ is observed as ______ – This is the source of the lines observed in the emission spectrum of H atoms. – The basic explanation holds for the spectra of other elements.

Atomic Spectra and BohrAtomic Spectra and Bohr

• The origin of atomic spectra is the movement of _________ between quantized energy states.

• Electron is excited from a lower energy state to a higher one – Energy is ________.

• Electron moves from a higher energy state to a lower one – Energy is _________.

∆∆E = Efinal – Einitial = -R h c( )1 1-

n2final n2

initial

Electronic Transitions in an Electronic Transitions in an Excited H AtomExcited H Atom

• If electrons move from energy states n >1 to the n =1 state – emission lines have energies in the UV region (Lyman series).

• If electrons move from energy states n >2 to the n =2 state – emission lines have energies in the VIS region (Balmer series).

• If electrons move from energy states n >3 to the n =3 state – emission lines have energies in the IR region.

Calculate the wavelength of the photon emitted Calculate the wavelength of the photon emitted if an electron in the H atom moves from if an electron in the H atom moves from n n = 4 = 4

to to n n =2=2

Flaws in Bohr’s TheoryFlaws in Bohr’s Theory

• Bohr’s model of the atom explained only the spectrum of H atoms and of other systems having one electron (such as He+).

• The idea that electrons are particles moving about the nucleus with a path of fixed radius, like that of the planets about the sun, is no longer valid.

Wave MechanicsWave Mechanics

Louis de Broglie (1892-Louis de Broglie (1892-1987) proposed that all 1987) proposed that all moving objects have moving objects have _______ _______ __________________________________(1924). (1924).

For light: (1) E = mcFor light: (1) E = mc22

(2) E = (2) E = h h vv = = h h c / c /

Wave Mechanics –Wave Mechanics –Calculate the Broglie WavelengthCalculate the Broglie Wavelength

Baseball (115 g) at 100 mph

e- with velocity = 1.9 x 108 cm/sec

It is possible to observe wave-like properties only for particles of extremely __________, such as protons, neutrons, and electrons.

= hm v

The Uncertainty PrincipleThe Uncertainty Principle

• Erwin Schrödinger, 1887-1961 : developed ________________or ______________.

• Werner Heisenberg, 1901-1976 : The uncertainty principle – it is impossible to fix both the ______________ electron in an atom and its ________ with any degree of certainty.

• Max Born, 1882-1970 : if the energy of an electron in an atom is known with a small uncertainty, there will be large uncertainty in its position in the space about the atom's nucleus.

• We can assess only the likelihood, or probability, of finding an electron with a given energy within a given region of space.

Schrödinger's Wave Schrödinger's Wave FunctionsFunctions

1. The behavior of the electron in the atom is best described as a standing wave – In a vibrating string, only certain vibrations can be observed = only certain wave functions are allowed for the electron in the atom.

2. Each wave function () is associated with an allowed energy value, En, for the electron.

3. Then, from 1 and 2, the energy of the electron is quantized – only certain values of energy.

Wave motion:Wave motion:wave length and wave length and

nodesnodes

4. In contrast to Bohr’s theory – quantization is imposed as a postulate.

Schrödinger's Wave Schrödinger's Wave FunctionsFunctions

5. The is related to the probability of finding the electron within a given region of space = _______________.

6. Energy is known precisely – position is given by a probability. The region of space in which an electron of a given energy is most probably located is called its _______________.

7. The solution to the Schrödinger's equation, for an electron, in a 3-D space, are 3 integer numbers = quantum numbers n, l, and ml. These numbers have only certain combination of values.

Quantum numbersQuantum numbers• n, Principal quantum number = 1, 2, 3, …Determines the ________ of the electron. Also related to size of

orbital.En = - Z2h R / n2

Electrons with the same n value are in the same electron ______ or same electron _________.

• l, Angular Momentum quantum number = 0, 1, 2, 3, …, n-1

Determines the ______ at which electrons circulate about the nucleus. Related to orbital __________.Electrons with the same l value are in the same _______ and have the same orbital _____ (______). All orbitals in the same subshell have the same ___________.

• ml, Magnetic quantum number = 0, ±1, ± 2, ± 3, …, ±l

Determines the _____________ of the orbital motion of the electron. (Clockwise or counterclockwise). Related to ___________ in space of the orbitals within a subshell, this gives the ___________ of orbitals in a subshell.

See Table 7.1 (p 319)

Quantum numbers and OrbitalsQuantum numbers and Orbitals

Number of subshells in a shell = nNumber of orbitals in a subshell = 2l + 1Number of orbitals in a shell = n2

l =0 (s) ; l =1 (p) ; l =2 (d) ; l =3 (f)Name of orbital = value of n and letter code

for lIf n=1 ; l = n-1 = 0 ; ml = 0Only 1 subshell (s); only 1 orbital (1s)

If n=2 ; l = 0, 1 ; ml = +1, 0, -1There are 2 subshells (s and p)4 orbitals (the 2s, and three 2p (3 orientations)

OrbitalsOrbitals

• Electron orbitals are probabilities – represented as ____________________.

OrbitalsOrbitals

• For the s orbital, the probability of finding an electron is the same at the same distance from the nucleus – the 1s orbital is ____________ in shape.

• Quantum mechanics – electron has wave properties – the maximum amplitude of the electron wave occurs at 0.053 nm from the nucleus.

• Bohr’s radius = 0.059 nm

surface density plotor radial distribution plot

OrbitalsOrbitals

• The p orbitals have 1 nodal surface – zero probability of finding an electron.

• Number of nodal surfaces = value of l• There are three p orbitals in each p subshell: ml = +1, 0,

-1• Refer to orbitals according to the axes along which the

lobes lie: px, py, pz

OrbitalsOrbitals

• The d five orbitals, l=2 have 2 nodal surfaces (may not be flat).

• What type of orbital is designated n = 4, l = 3, ml =-3?

a. 4sb. 4pc. 4dd. 4fe. none

OrbitalsOrbitals

Students should be familiar with definitions of quantum numbers and

orbital types.

PracticePractice

• Which of the following represent valid sets of quantum numbers?

a) n=3, l=3, ml= +1

b) n=5, l=1

c) n=6, l=5, ml=1

d) n=4, l=3, ml=-4

RememberRemember

• Go over all the contents of your textbook.

• Practice with examples and with problems at the end of the chapter.

• Practice with OWL tutors.• W ork on your assignment for

Chapter 7.• Practice with the quiz on the cd or

online service.