Chapter 7: Electronic Chapter 7: Electronic StructureStructureElectrons in an atom determine

virtually all of the behavior of the atom.

Quantum theory – the study of how energy and matter interact on an atomic level.

To understand the electron, we must first understand light.

Reason =

LightLightAlso known as electromagnetic

radiation.Ex) Visible light, Infrared, X-ray,

Radio.All electromagnetic radiation have

several common characteristics.◦Light as a wave◦Light as a particle◦“Duality of Light”

Electromagnetic RadiationElectromagnetic Radiation

Light as a WaveLight as a WaveWavelength ( – lambda) = Frequency ( – nu) =

Light as a WaveLight as a Wave•Wavelength and Frequency are inversely related.

Electromagnetic SpectrumElectromagnetic SpectrumShows the full range of

electromagnetic radiation that exists.

Light as a WaveLight as a WaveThe product of the wavelength

and the frequency, though, is a constant.

c = , where c is the speed of light.

Thus, if we know the frequency, we can find the wavelength and vice versa.

LEP #1(a).

Proof of WavesProof of WavesWaves exhibit certain properties

when they interact with each other.Young’s Double Slit experiment.

Proof of WavesProof of Waves

Proof of WavesProof of Waves

Light as a ParticleLight as a ParticleThe wave nature of

light does not explain all of the properties of light.

Blackbody radiation – when solids are heated, they will glow.

Color depends on the temperature.

Light as a ParticleLight as a ParticleMax Planck – proposed a theory

that energy from blackbody radiation could only come in discrete “chunks” or quanta.

E = h h = 6.626 x 10-34 JsLEP #1(b).

Light as a ParticleLight as a ParticleThe

photoelectric effect (Einstein) also is proof that light must have a tiny mass and thus act as a particle (photon).

LEP #2, #3.

Line SpectraLine SpectraWhen a gas

like H2, Hg, or He is subjected to a high voltage, it produces a line spectrum consisting of specific wavelengths.

Line SpectraLine Spectra

High Voltage ExcitationHigh Voltage Excitation

Identifying MetalsIdentifying Metals

Na = yellow K = violet Li = red Ba = pale green

Line SpectraLine SpectraThe four lines for hydrogen were

found to follow the formula:

Where the values of n are integers with the final state being the smaller integer.

72 2f i

1 1 1 = 1.097 10 / m -

λ n n

Bohr TheoryBohr TheoryHow could such a simple

equation work?Niels Bohr some thirty years later

came up with a theory.Classic physics would predict that

an electron in a circular path should continuously lose energy until it spiraled into the nucleus.

Bohr TheoryBohr Theory1. An electron can only

have precise energies according to the formula: E = -RH / n2 ; n = 1, 2, 3, etc. and RH is the Rydberg constant.

2. An electron can travel between energy states by absorbing or releasing a precise quantity of energy.

Bohr TheoryBohr Theory

Bohr TheoryBohr TheoryCan not explain the line spectra

for other elements due to electron-electron interactions.

Thus, the formula for Hydrogen can only be applied for that atom.

LEP #4.

Matter as a WaveMatter as a WaveLouis de Broglie proposed that if

light could act as both a wave and a particle, then so could matter.

Where h is Planck’s constant, m is the objects mass, and v is its velocity.

Size, though, matters. LEP #5.

hλ =

mv

Matter as a WaveMatter as a WaveDe Broglie was later proven correct

when electrons were shown to have wave properties when they pass through a crystalline substance.

Electron microscope picture of carbon nanotubes.

Uncertainty PrincipleUncertainty Principle

German scientist Werner Heisenberg proposed his Uncertainty Principle in 1927.

History

Uncertainty PrincipleUncertainty PrincipleFor a projectile like a bullet, classic

physics has formulas to describe the motion – velocity and position – as it travels down range.

Uncertainty PrincipleUncertainty PrincipleAny attempt to observe a single

electron will fail.

Uncertainty PrincipleUncertainty PrincipleIf you want to measure length, there is

always some uncertainty in the measurement.

To improve the certainty, you would make a better measuring device.

Heisenberg, though, stated that the precision has limitations.x mv h / 4

Uncertainty PrincipleUncertainty Principle

Once again, size makes a big difference.

LEP #6

Uncertainty PrincipleUncertainty PrincipleDeterminacy vs. IndeterminacyAccording to classical physics, particles

move in a path determined by the particle’s velocity, position, and forces acting on it◦ determinacy = definite, predictable future

Because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow◦ indeterminacy = indefinite future, can only

predict probability

Uncertainty PrincipleUncertainty Principle

Quantum MechanicsQuantum Mechanics

The quantum world is very different from the ordinary world.

Millions of possible outcomes and all are possible!

Quantum Café“I am convinced that He (God)

does not play dice.” Albert Einstein

HH = E = EErwin Shrödinger proposed an

equation that describes both the wave and particle behavior of an electron.

The mathematical function, , describes the wave form of the electron. Ex) a sine wave.

Squaring this function produces a probability function for our electron.

Atomic OrbitalsAtomic OrbitalsA graph of 2 versus the radial

distance from the nucleus yields an electron “orbital”.

An “orbital” is a 3D shape of where an electron is most of the time.

An “orbital” can hold a maximum of two electrons.

Atomic OrbitalsAtomic OrbitalsThe Probability density function

represents the probability of finding the electron.

Atomic OrbitalsAtomic Orbitals•A radial distribution plot represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus•The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases

Atomic OrbitalsAtomic OrbitalsThe net result for the

Hydrogen electron is a most probable distance of 52.9pm.

Atomic OrbitalsAtomic OrbitalsFor n=2 and beyond, the orbital

will have n-1 nodes.A node is where a zero

probability exists for finding the electron.

Atomic OrbitalsAtomic Orbitals

2s orbital = 1 node

3s orbital = 2 nodes

Quantum NumbersQuantum Numbers An electron can be described by

a set of four unique numbers called quantum numbers.

1. Principle quantum number, n = describes the energy level of the electron. As n increases so does the energy and size of the orbital. n can have values of integers from 1 to infinity.

Quantum NumbersQuantum Numbers

2. Azimuthal quantum number, l, defines the shape of the orbital. The possible values of l depends on n and can be all of the integers from 0 to n-1. However, the values of 0, 1, 2, and 3 have letter designations of s, p, d, and f, respectively.

Quantum NumbersQuantum Numbers

3. Magnetic quantum number, ml

describes the orientation in space of the orbital. The possible values of this quantum number are –l 0 +l. When l is not zero, the magnetic q.n. has more than one value. These multiple values produce degenerative orbitals – orbitals of equal energy.

Quantum NumbersQuantum Numbers

4. Spin quantum number, ms

describes the electron spin of the electron. This value is either +1/2 or –1/2.

Quantum NumbersQuantum Numbers

Quantum NumbersQuantum NumbersPauli Exclusion Principle – no

electron in an atom can have the same set of four quantum numbers.

Ne = 10 electronsLEP #7.

Subshell DesignationsSubshell Designations

Value of

l0 1 2 3

Type of

orbitals p d f

OrbitalsOrbitals

s type orbitals are spherical in shape.

OrbitalsOrbitals

p type orbitals have two lobes.

OrbitalsOrbitals

d type orbitals generally have four lobes.