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CHAPTER 6ELECTRONIC STRUCTURE OF

ATOMS

The Wave Nature of Light

• All radiated energy can be thought of as a wave

• The waves are electromagnetic in nature (they are caused and effected by both electrical charge and magnetic fields)

• All these waves travel at the same speed, the speed of light (which is an electromagnetic radiation)

• The distance from the top of one wave to the top of the next one is the wavelength

• The number of waves that pass a point each second is the frequency

• The height of the wave is the amplitude


• The Electromagnetic Spectrum lists the “names” of different types of waves by their wavelength and frequency


• From the last picture, it is obvious that wavelength and frequency are related

• Remember that all emag waves travel at the same speed

• At the same speed, the waves with less distance to travel pass by my point more often.

• The equation for frequency (ν) and wavelength (λ) is

c= ν* λ• Frequency is measured in Hertz (s-1)


• Did you grandmother or mother ever say “Don’t touch that stove it’s red hot!”?

• When you take something and heat it up it, at some high temperature it will start to give off visible light, red to start.

• This is called black body radiation since the thing was black when we started.

• The question is how much energy is given off at a specified temperature?

Quantized Energy & Photons

• Normally, the energy given off is thought of as a bell curve, with there being tiny amounts of high energy (high frequency) waves, more and more middle energy waves, and tiny amounts of low energy waves.


• X represents the average wavelength given off, and notice how the wave lengths should tapper off as they get larger and smaller.

• What’s the problem with this?


• The bell curve NEVER reaches 0.

• The area under the curve is infinite since it keeps going.

• The area under the curve represents the total energy given off.

• Objects DO NOT each give off infinite amounts of energy.

• So what is really happining?


• Enter Max Plank• His theory is that energy can only be given off in

“pieces” of a minimum (whole number) amounts.

• In Latin, the word the word for fixed amount is QUANTUM.

• Now, when we get to the right of the bell curve, you reach a point where the object does not have enough energy left to emit another stronger quanta.

• The object no longer emits infinite energy


• Plank proposed that the energy of any quanta is equal to it’s frequency time a constant:

E=hv

• h is called Plank’s constant and

h=6.626x10-34 Js (joule seconds)


• According to Plank’s theory, energy can only be emitted in whole number multiples of hv (hv, 2hv, 3hv, …).

• Now, I know I said light can be thought of as a wave ten slides ago, but now let’s think of it a a particle, called a photon.

• The energy of the photon is given by Plank’s law E=hv

• Plank’s law can be written for wave length since v=c/λ E=hc/λ


• Now let’s look a an electron orbiting an atom.

• The electron is held on by a fixed amount of energy (it were held infinitely tight, there could be no sharing or transfer of electrons needed for chemical reactions)

• If the electron is hit by a photon with more energy then the atom is holding it by, the electron is ejected from the atom.


• When a photon bumps an electron out of an atom it is called the photoelectric effect.

• This is how solar cells work.

• Metals are usually the only atoms that give off electrons.

• Each metal has a different minimum energy (more to follow)


• If you shine a white light through a prism a full spectrum is generated

Line Spectra & the Bohr Model

• If you shine a lamp made with an elemental gas (neon) or vaporized element through a prism, only a few lines are generated.

• These are called Spectral Lines



• Rydberg figured out an equation to relate the 4 lines of the hydrogen spectrum:

17

21

22

21

10*096776.1

integers positive are n and n

constant Rydberg thecalled is

111

mR

R

nnR

h

h

h

Why don’t electrons “fall” into the nucleus of an atom? Bohr came up with a model of the atom that explained this and the spectral lines:

1. Only electron orbits of certain radii (corresponding to definite energies) are allowed.

2. Electrons in an allowed orbit will not radiate energy (so they can’t spiral into the nucleus).

3. Energy is only absorbed or emitted when electrons move from one allowed orbit to another. The energy is emitted as a photon, E=hv


• Bohr combined the equation for motion, electrical charges, and emission energy, and came up with:

E=(-hcRh)(1/n2)• H is Planks constant, Rh is Rhdberg’s constant,

and c is the speed of light so if we put those numbers in we get:

E=-2.18*10-18 (1/n2) J• n is a number from 1 to ∞ called the quantum

number


• E=-2.18*10-18 (1/n2)• When n=1 (the smallest it can be) the

electron is in the ground state, and • E=-2.18*10-18 J• What happens when the electron moves

infinitely far away? (1/n2) becomes 0 so E=0. This is called the zero energy state (really imaginative name)

•


• Why is the lowest (ground) state negative and the highest zero?

• Higher orbits have greater energy

• Electrons “want” to be close to nuclei


• What happens if an electron absorbs energy and gets “bumped” up to a higher energy level?

• The electron is in a high energy state, but things like to be in the lowest energy state, so it gives off the energy according to the emission rules



emitted. lines

spectral theare s wavlengthThese falls.

electron thestatesenergy ofnumber the

on based ts)(wavelengh sfrequencie

specific of potons emitts tom theSo

1110*18.2

so and

2218

a

nn

hcE

cvhvEEEE

if

photoninitfinal

• Limitations of the Bohr model:1. It only explains the spectral lines of

Hydrogen2. Saying the electron won’t fall into the

nucleus because it can’t isn’t good enough

• So thinking of an electron as a planet circling a sun is not that good of an idea

• Where have you heard that before?


• Wave – Particle; Particle – Wave: which is it all ready!!!!

• Well either or both, don’t ask me why• Try reading In Search of Schrodinger's

Cat: Quantum Physics And Reality by John Gribin sometime.

• Short answer, if you look for a wave, you find a wave, if you look for a particle, you find a particle.

Wave Behavior of Matter

• New guy De Broglie decides to look at electrons as waves.

• The electron would have a wavelength • De Broglie proposed that the wavelength

depended on the mass and velocity of the electron:

Λ=h/mv• mv for any object is it’s momentum• ANY object has a wavelength, even you and I,

but our wavelength is too small to observe


• The uncertainty principle – Heisenberg

• If I roll a bowling ball down a ramp, I can measure it’s position and velocity at any time. I know these things because photons of light bounce off the ball, travel to my eye, and I can see the ball to measure these things.


• What if I roll an electron down a ramp?• The photons that hit it move it.• When the photons reach my eye, the

position of the electron has changed.• I don’t know exactly where the electron is.• Long story short, I can either know the

position or the momentum well, by the equation:

∆x * ∆mv ≥h/4π


• Question: you have to memorize some of the formulas in the chapter, you can either memorize all the one’s you have all ready learned or the next one, you can decide.

• Just think about it and I’ll tell you when you need to decide.

Quantum Mechanics & Atomic Orbitals

• Schrodinger came up with an equation to describe electron (or any particle) waves

• This opened a new way of looking at particles called wave or quantum mechanics

• If you pluck a guitar string a wave travels up and down the string; this is called a standing wave

• Schrodinger came up with an equation to describe a function to describe the electron’s probable position on an allowed energy state

• (Ok, now you have to decide on the equations)


• The Schrodinger wave equation describes the probability of an electron’s position when in a given allowed energy state.


• Solving the wave equation gives a list of densities where an electron can be found when in a particular energy state.

• The densities associated with an energy is called an orbital (orbital ≠ orbit)

• The Bohr model used one quantum number (n) to describe the energy state, quantum mechanics uses three, n, l, and m



1. The principal quantum number (n) can have positive integer values. The bigger n is, the higher the energy of the electron

2. The second number (l) is the angular momentum number.

a. It can have values from 0 to (n-1).b. Each number has a differently shaped orbitalc. Each number (l) for a given orbital (n) is

designated by a letter

l= 0 1 2 3

Letter s p d f


3. m is the magnetic quantum number. m can have integer values from –l to l

• Each principal quantum number, n, is called the shell

• Each shell has sub-shells. The number of sub-shells equals the shell number. The sub-shells correspond to l

• Each sub-shell has orbitals equal to m (that makes 2l+1 orbitals)



n (shell)

Possible values of l

Sub shell designation

Possible values of m

Orbitals in sub shell

Total orbitals in the shell

1 0 1s 0 1 1

2 0 2s 0 1

1 2p -1,0,1 3 4

3 0 3s 0 1

1 3p -1,0,1 3

2 3d -2,-1,0,1,2 5 9

4 0 4s 0 1

1 4p -1,0,1 3

2 4d -2,-1,0,1,2 5

3 4f-3,-2,-1,

0,1,2,3 7 16

• The s orbitals• The wave function yields a shape that is

like a hollow sphere centered at the nucleus

• It’s not an “M&M” shell, more like a fuzzy tennis ball

• As n increases, the shell expands, kind of• The wave equation indicates areas of

probability outside of the “ball’s surface”

Representing Orbitals


• p orbitals – They have two teardrop lobes– The lobes DO NOT TOUCH– The three orbitals are arranged on the three

axis and called px, py, and pz



Actual probability distribution for a p orbital. Notice there are no dots at x=y=z=0

• d and f orbitals– When n=> 3, d orbitals are formed– There are five of them– Four look like 4 – leaf clovers, the other like a

p orbital with a belt.



• f orbitals occur when n=>4

• There are 7 of them

• Just know that there are there



• Unlike the Hydrogen atom, other atoms have more then one electron.

• When you look at the spectral lines from these atoms, there are actually TWO closely spaced lines.

• It was postulated that each orbital had TWO electrons.

• So a new quantum number, the spin magnetic number (ms) was created

• ms can have a value of +1/2 or -1/2

Electron Spin

• Pauli exclusion principle – no two electrons in an atom can have set of four quantum numbers.

• That means each orbital can have 2 electrons in it.

• Lithium (Li) has three electrons:– Li n1, s, ms1/2

n1, s, ms-1/2 n2, s, ms ½

• Orbitals are filled from LOWEST to HIGHEST as we will see next

Electron Spin

• How do we diagram the electron configuration?

• Each orbital in an atom is represented by a box.

• The boxes are arranged in order of increasing energy

• Each box can have 2 arrows (↑↓), one for each magnetic spin number

Electron Configuration


• s orbitals take both electrons before the p orbital starts filling

• Higher orbitals like p and d fill up one electron at a time – i.e. one electron in each orbital until they all have one, then back to the beginning the second electron.



• Condensed notation• By the time you get to the third period,

there’s a lot of orbitals to write.• To save time, we write the noble gas from

the last period, then start with the new shell.

• Remember that the noble gas from the period above has all the orbitals up to tht point full.



Each [Ne] represents the shells 1s2 2s2 2px2 2py2 2pz2. It’s a lot easier to write [Ne]

• Transition metals fourth period– Both s orbitals get filled first– Next the period THREE d orbitals get filled– Then the period 4 p orbitals get filled

• Series metals (period 6)– Both 6s orbitals get filled first– Next one 5d orbital get filled– Then the 4f orbitals get filled– Then back to the 5d orbitals– Then pack to the 6p orbitals

• This is confusing and you will never use this again unless you study chemistry.


Electron Configuration & the Periodic Table

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