Electrons in atomsChapter5

Waves

• Light travels as both Waves and Packets of energy.

• Light is a form of Electromagnetic Radiation.– EM Radiation has

waves in the electric and magnetic fields

• All waves (Water or Electromagnetic) have 4 key characteristics:– Amplitude

– Wavelength

– Frequency

– Speed

Wave Characteristics

• Amplitude.– Height of a wave from

origin to a peak/crest.

– Affects brightness and intensity.

• Wavelength.– Distance from crest to crest.

Distance for one full cycle.

– Visible light: 400-750nm.

Wave Characteristics

• Frequency.– How fast a wave oscillates

(moves up and down).

– Units: s-1, 1/s or Hz.

• Speed.– Speed of light (in a

vacuum) is constant:

3.00 X 108 m/s.

• Frequency and Wavelength related by the equation: = c /

Try this…

If the frequency of a wave is 93.1 x 106 s-1, what is the wavelength?

Answer: 3.22 m

If the wavelength of a wave is 1.54 mm, what is it’s frequency?

Answer: 1.95 x 1011 Hz (s-1)

Have a Problem?

Rearranging the equation:

• First, multiply by (frequency): = (c/)

• Now, divide by (wavelength):() / = c /

• Leaving: = c/Moving on….

Electromagnetic Spectrum

• Many parts including:– Gamma Rays (10-11 m)

– X-Rays (10-9 m)

– Ultra-violet (10-8 m)

– Visible (10-7 m)

– Infared (10-6 m)

– Microwave (10-2 m)

– TV/Radio (10-1 m)

Electromagnetic Spectrum

• Visible Spectrum:ROY G BIV

– Red

– Orange

– Yellow

– Green

– Blue

– Indigo

– Violet

Electromagnetic Spectrum (once more)

Modern Atomic Theory

Quantum Theory

Early Puzzlements

• Wave model for light was originally accepted by scientific community.

• This couldn’t explain why metals heating first emitted invisible radiation and then visible radiation.

• Other questions included why elements only emitted certain characteristic colors of light.

Planck’s Theory

• Every object can only absorb or emit a fundamental amount of energy.

• This amount is called a quantum.

• The amount is like moving up or down steps.

Planck’s Theory

• Planck’s Theory is based on the relationship between frequency and the energy of the particle.

• E = h• Plank’s Constant:

– h = 6.6262 X 10-34 J-s

Quick Practice

If a wave has a frequency of 9.33x106 Hz, what is it’s energy?

6.18x10-27 J

What is the frequency of a wave if its energy is 4.32x10-31 J?

652 Hz

Photoelectric Effect

• Einstein used Plank’s equation to explain a puzzling phenomenon, the Photoelectric Effect.– Electrons ejected from metal when light shines on it.

– Metal need’s certain frequency of light to release electrons. In Sodium, red light is no good, violet releases them off easily.

– Photons: Tiny particles of light providing energy to “knock off” electrons.

Dual Nature of Radiant Energy

• Summary:– Light behaves as a

wave ( = c/)– Light behaves as a

particle (E = h)

Modern Atomic Theory

Another Look at the Atom

Line Spectra

• Def: A spectrum that contains only certain colors/wavelengths.

• AKA: The Atomic Emission Spectrum

• Each element has it’s own “fingerprint” emission spectrum.

The Bohr Model

• Bohr drew the connection between Rutherford's model of the atom and Planks idea of quantization.

• Energy levels labeled with Quantum Numbers (n)

• Ground state, or lowest energy level – n=1

• Excited State – level of higher energy

Matter Waves• If energy has dual nature, why not matter?• 1924: De Broglie introduced his theory of electron

waves– Included his wave-particle duality theory of matter

• His thesis examiners were unsure of the material, and passed it onto Einstein for evaluation. Einstein wholeheartedly endorsed the theory.

• The research resulted in the “de Broglie Hypothesis”– “Any moving particle or object has an associated

wave”

de Broglie equation (simplified)

• De Broglie Equation:λ= h/mv

λ: Wavelength

h: Planck’s Constant (6.6262 X 10-34 J·s)

m: mass

v: velocity

Schrodinger• Erwin Schrodinger built off de Broglie’s idea and

wrote mathematical equations as wave functions.• When these equations are solved, we get what are

called “orbitals”– Orbitals are regions of space that describe the

probability of finding an electron in a particular location

– While Bohr’s model was 1 dimensional, Schrodinger’s model allowed the electron to occupy 3D space

– It is Schrodinger’s wave equations that provide the principal, angular, and magnetic quantum numbers

• Schrödinger Wave Equation (1926)

– finite # of solutions quantized energy levels

– defines probability of finding an e-

σ3/2 Zπ

11s 0

eΨ a

No, you don’t need to know this equation…Just what it is used for.

Orbital (“electron cloud”)• Region in space where there is 90%

probability of finding an electron.

Orbital Radial Distribution Curve

Heisenberg Uncertainty

• Uncertainty Principle– The position and momentum of a moving

electron cannot simultaneously be measured and known exactly.

• Translation:– Cannot know exactly where and how fast an

electron is moving at the same time.

Modern Atomic Theory

A New Approach to the Atom

Quantum-mechanics Model

• Includes all the ideas of the atom we have covered:– Energy of electrons is quantized– Electrons exhibit wavelike behavior– Electrons position and momentum cannot be

simultaneously known– Model does describe the probable location of

electrons around the nucleus

Probability and Orbitals

• Electron Density:– The density of an

electron cloud.

• Atomic Orbitals:– A region around the

nucleus of an atom where an electron with a given energy is likely to be found.

• Kinds of orbitals:– Each kind has own

different basic shape.– Given letter

designations of s, p, d and f.

– s-orbitals are spherical– p-orbitals are dumbbell– d- and f-orbitals more

complex.

Quantum Numbers• 4 quantum numbers

– Specify the “address” of each electron in an atom

Quantum Numbers

• Principle Quantum Number (n)– Energy level– Size of the orbital– n2 = # of orbitals in the

energy level

Quantum Numbers• Angular Momentum Quantum Number ( l )

– Energy sublevel– Determines shape of the orbital– Can be any integer between 0 and n-1

s p d f

l = 3

l = 0

l = 2

l = 1

Correlation of n & l

Principle quantum

number (n)

# of Sublevels

Angular quantum

number (l)

Sublevels referred to

as:

1 1 0 s

2 2 0, 1 s, p

3 3 0, 1, 2 s, p, d

4 4 0, 1, 2, 3 s, p, d, f

Quantum numbers

• Magnetic quantum number ( ml )

– Determines orientation of orbital– Specifies exact orbital within each sublevel– Can be any integer between –l and +l

Quantum numbers

pzpypx

Quantum numbers

• Spin quantum number ( ms )

– Electron spin either +½ or -½– An orbital can hold 2 electrons that spin in

opposite directions

Quantum Numbers• Pauli Exclusion Principle

– No 2 electrons in an atom can have the same 4 quantum numbers.

• Example:• An atom of Magnesium has 12 electrons and is

located in period 3. List all sets of possible quantum numbers.– n = – l could be:– ml could be:– ms could be:

30, 1, 2-2, -1, 0, +1, +2+½ OR -½

Modern Atomic Theory

Electron Configurations