Light

A form of electromagnetic radiation

Composed of perpendicular oscillating waves

(one = electric field, other = magnetic field)

Electric field

A region where an electrically charged particle experiences a force

Magnetic field

A region where a magnetized perticle experiences a force

Speed of light

c

c = 3.00 × 10^{8} m/s

Wavelength

λ (lambda)

The distance between identical points on successive waves

*Inversely proportional to frequency

Amplitude

The verticle distance from the midline of a wave to the peak (or trough)

A measure of light **intensity**

*Directly proportional to total energy of wave

(larger amplitude = more force)

Frequency

*v* (nu)

*v* = c / λ

The number of waves that pass through a particular point in a given period of time

hertz (Hz) or cycles per second (1 s^{-1})

1 Hz = 1 s^{-1}

*Directly proportional to total energy of a wave

(More frequency = more total force)

*Inversely proportional to wavelenth

Electromagnetic spectrum

Low energy to high:

radio

microwave

infared

visible light

ultraviolet

X-ray

gamma ray

Interference

The interaction between waves

Constructive interference

Occurs when waves that are *in phase* interact so that they add to make a larger wave

*Amplitudes are summed making the larger wave

Destructive interference

Occurs when waves that are *out of phase* interact so that they cancel each other out (flat line)

Diffraction

Occurs when a traveling wave encounters an obstacle or opening in a barrier that is about the same size as its wavelengh and it bends (diffracts) around it

*Waves diffract

**Particles DO NOT diffract (they just pass through opening)

Interference pattern

Inherent characteristic of all waves

Light is diffracted through two slits creating an alternating pattern

Photoelectric effect

The observation that many metals emit electrons when light shines on their surface

Quanta or photons

Light energy delivered to atoms in "packets"

Photon energy

E

E = hv

v = c/λ

Thus:

**E = hc/λ**

Planck's constant

h

h = 6.626 × 10^{-34} J×s

Threshold frequency

Reached when the energy of a photon is equal to the binding energy of emitted electron

h*v* = Φ

or E = Φ

Binding energy of emitted electron

Φ (phi)

Kinetic energy of an ejected electron

KE = h*v* - Φ

Excess energy of a photon that is transferred to an electron in the form of kinetic energy

Wave-particle duality of light

Sometimes light appears to behave like a wave, other times like a particle

Behavior observed depends on experiment

Number of photons

Number of photons = E_{pulse} / E_{photon}

*E_{photon} = hc/λ

Atomic spectroscopy

The study of the electromagnetic radiation absorbed and emitted by atoms

Emission spectrum

The "fingerprint" of an element in the form of a series of bright lines

Can be used to identify an element

Bohr model of the atom (4)

1. Energy of atom is quantized (can only have very specific amounts of energy

2. Amount of energy in atom relates to electron's position in atom

3. Electrons travel in orbits/fixed distance from nucleus

*Energy of electron proportional to distance

4. Electrons emit radiation when they "jump" from an orbit with higher energy down to lower energy orbit

*Distance determins energy of photon of light produced

de Broglie relation

Wavelength inversely proportional to momentum (m*v*)

λ = h/m*v*

(Wavelength = h/mass * frequency)

Complimentary properties

The more you know about one property, the less you know about the other

When **wave** **nature** (interference pattern) is observed, **particle** **nature** (position/which slit electron passes through) cannot be, and vice versa

Heisenberg uncertainty principle

Product of uncertainties in both position and speed of a particle is inversely proportional to its mass

Δx × mΔ*v* ≥ h/4π

Δx = position uncertainty

Δ*v* = velocity uncertainty

m = mass

Indeterminacy

Indefinite future = can only predict **probability**

Orbital

A probability distribution map of a region where the electron is likely to be found

Quantum numbers (4)

1. Principal quantum number, n

2. Angular momentum quantum number, l

3. Magnetic quantum number, m_{l}

4. Spin quantum number, m_{s}

Principal quantum number

n

Indicates the orbital (Bohr's energy level)

*As n gets larger, amount of energy between orbitals gets smaller

Equation for energy of a hydrogen electron

**E _{n} = -R_{H} (1/n^{2})**

R_{H} is Rydberg constant for hydrogen

R_{H} = 2.18 × 10^{-18} J

Angular momentum quantum number

l

Angu**l**ar momentum = what kind of/angle of orbit

**l =** 0, 1,... **n-1**

l = 0 → s

l = 1 → p

l = 2 → d

l = 3 → f

e.g.

n = 2

l = [0, 1]

Magnetic quantum number

m_{l}

**m _{l} = [-l, l]**

e.g.

n = 2

l = [0, 2] → d orbital

m_{l} = [-2, 2] → 5 d orbitals

Spin quantum number

**m _{s}**

Specifies the orientation of the spin of the electron

Value is either:

+1/2 (spins up)

or

-1/2 (spins down)

Describing an orbital (3)

1. n, l, m_{l} describes one orbital

2. Orbitals with same **n** value = same **principal energy level** (shell)

3. Orbitals with the same values of **n & l** = same **sublevel** (subshell)

Equation for energy transition in hydrogen

ΔE = E_{final} - E_{initial}

**ΔE _{H atom} = -2.18 × 10^{-18} J (1/n^{2}_{final} - 1/n^{2}_{initial})**

Energy emitted by electron is carried away by the releated photon, thus:

**E _{photon} = -ΔE**

Probability density

The probability of finding an electron at a **particular** **point** in space

Probability decreases as distance from nucleus increases

Radial distribution function

**Total probability** of finding an electron at a **certain** **distance** *r* from the nucleus

Volume of shell also increases with distance from nucleus

Nodes

Where the probability drops to zero, for both probabilities

s orbital

l = 0

spherical shape

1 s orbital

p orbital

l = 1

shaped like two balloons

-1, 0, 1

3 p orbitals

d orbital

l = 2

shaped like four balloons

-2, -1, 0, 1, 2

5 d orbitals

f orbital

l = 3

shaped like eight balloons

-3, -2, -1, 0, 1, 2, 3

7 f orbitals