Electrons in Atoms:LIGHT & QUANTIZED

ENERGY

Review and Background• 400 B.C.E. – Democritus:

proposed that all matter is composed of “atomos”

(Review and Background, con’t)

• 1808 – John Dalton:Atomic Theory summed up experimental evidence for existence (and some behavior) of atoms.

(Review and Background, con’t)

• 1897 – JJ Thomson:o Cathode-Ray Tubeo Electron – negativeo ‘Plum-Pudding’ Model

(Review and Background, con’t)

• 1911 – Ernest Rutherford:o Gold-foil experimento Nucleus – positive, dense,

most of atom is spaceo ‘Nuclear’ model

(Review and Background, con’t)

• 1911 – Ernest Rutherford:New Zealand (his native country) honored his discovery of the nucleus with:

A. PROPERTIES OF LIGHT

A. Properties of Light

1. Before we can learn more about the atom, we need to have some background about the properties of light.

(A. Properties of Light)

Things move in one of two ways: 1. waves (like water)

2. particles (like BBs)

(A. Properties of Light)

2. Many of light’s properties can be explained by light moving in waves.

(A. Properties of Light)

3. Two types of waves:(1) Transverse(like waves of water)

(A. Properties of Light)

(2) longitudinal(like waves of sound or ‘rubber-neck’ traffic jam)

(A. Properties of Light)

4. Many of light’s properties can be explained by light moving in TRANSVERSE waves.

TRANSVERSE

WAVES

(A. Properties of Light)

Parts of a wave:

l (lamda) = wavelengthdistance between the same pointon two adjacent waves

l

(A. Properties of Light)

Parts of a wave:

Frequency (n; nu) how often the wave hits a given point

123456789n

(A. Properties of Light)

5. Electromagnetic (EM)

a. EM radiation = form of energy that exhibits wave-like behavior.

(A. Properties of Light)

5. Electromagnetic (EM)

b. EM spectrum = all forms of EM radiation.

(A. Properties of Light)

5. EM Radiation

c. Examples:

radio waves, cell phones,

microwaves, visible light,

radar, X-rays, g-rays

(A. Properties of Light)

Common Units:• Wavelength: visible light:

nanometers (109 nm = 1 m)

~ 400 nm - 700 nm

(A. Properties of Light)

Common Units:• Frequency: Hertz (Hz) (1 Hz = 1 cps) cycles per second (cps) 1/second = 1/s = s-1

s-1 = 1/second = 1 Hz

(A. Properties of Light)

Common Units:• Frequency (con’t): FM radio: MHz (x 106 Hz)

AM radio: kHz (x 103 Hz) electricity: 60 cps (USA)

(A. Properties of Light)

5. Frequency and Wavelength of EM radiation related:

c = l nwhere:

c = speed of light (3.0 x 108 m/s)

l = wavelength (m)

n = frequency (1/s = s-1)

(A. Properties of Light)

c = l nHow are l and n related? directly inversely neither both

(A. Properties of Light)

E = h n E = energy of a photon (quantum of EM radiation – specifically light)

h = Planck’s constant (6.626 x 10-34 J-s)n = frequency

Combining

E = h n and c = l nto solve for l when not given n

(A. Properties of Light)

E = h nHow are E and n related? directly inversely neither both

The Nuclear Model (Rutherford) of the atom was useful in modeling the electrons orbiting the nucleus. However, according to classical physics, an orbiting object loses energy and eventually spirals into the nucleus. (<1 sec for a atom)

This problem was solved by Niels Bohr

1. Bohr model of the atom.

2. Not precisely our current model of the atom, it’s extremely useful to explain the atom.

3. Used line-emission spectrum of hydrogen

http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/linesp16.swf

1. Classical physics: energy is emitted in a continuous spectrum.

2. Isn’t – line-spectrum

3. Quantum = small packets of energy(quanta = plural; photon = light packet)

Bohr:

1. Electrons are confined to fixed and discrete orbits.

2. Distance between orbits represents the energy emitted.

Bohr Model of the Atom

Electron is in ground state. Energy absorbed by electronsimultaneously moves electron to excited state.

Electron attracted to nucleus; falls down & enters lower energy level simultaneously emitting energy.

Electron eventually returns to ground state. (Jumping down stairs: all at once, or more slowly)

Only specific & fixed orbits are allowed in the Bohr model of the atom.

What keeps the electrons in specific orbits?

The duality of wave-particle behavior Our frame of reference: particles or waves Quantum mechanics: dual wave-particle

The allowable electron orbits are like standing waves.

A vibrating guitar string is constrained to vibrate between two fixed points.

(b) Possible vibrations limited to multiples ofhalf-wavelengthsQuanta= ½ wavelength.

(c) Possible electron orbits:Limited to whole numbers of complete

wavelengths

electron wave no whole number= allowed orbit(n=4) = orbit not allowed

(c) Possible electron orbits:Limited to whole numbers of complete

wavelengths

Brief summary:• Line-emission spectrum (showed quanta of energy)• Bohr model (differences in energy levels = quanta)• wave-particle (orbits are standing waves)

• Heisenberg Uncertainty Principle

Brief summary:• Line-emission spectrum (showed quanta of energy)• Bohr model (differences in energy levels = quanta)• wave-particle (orbits are standing waves)

• Heisenberg Uncertainty Principle“It is impossible to know simultaneously both the

location and momentum of a particle.”

Δ𝑥 ∙ Δ𝑝𝑥≥ℏ2

• Thus where the electron is at any given time is a probability.

Heisenberg Uncertainty Principle:One cannot know simultaneously both the location & momentum of a particle.

Current Model of the Atom:• Schrödinger Wave Equation

(shown here only for you to see it is a complex mathematical equation)

• The solution is psi () which gives the location & momentum of an electron in x-, y-, z-, & time-coordinates.

Current Model of the Atom:• Bohr model versus wave equation

1. fixed orbits probable locations

2. 2-D orbits 3-D orbitals

N.B. Nucleus not shown to scale.

El include 4 quantum numbers:• n: principal quantum number

(= principal energy level

(= period on periodic table) • ℓ: magnetic quantum number (shape of orbital)

• mℓ: angular quantum number (orientation)

• s: spin (+½ or – ½; or )

The solution to Schrödinger’s is psi () which gives the location & momentum of an electron in x-, y-, z-, & time-coordinates.

El

Energy levels for the principal quantum number (n):