Chapter 5

Electrons in Atoms

Wave Nature of Light

• Electromagnetic radiation which is a form of energy that exhibits wavelike behavior as it travels through space.

• Examples: light, radio waves, x-rays, etc

Parts of a Wave

wavelength

amplitude

amplitude

crest

trough

wavelength

origin

Wavelength

• Waves have a repetitive nature.• Wavelength- ( lambda)

– shortest distance between corresponding points on adjacent waves.

– Measured in units like meters, centimeters, or nanometers depending on the size.

– 1 x 10-9 meters = 1 nanometer

Frequency• # of waves that pass a given point per

second.• Units are waves/sec, cycles/sec or

Hertz (Hz)• Abbreviated the Greek letter nu or

by an f

c = f

Frequency and wavelength

• Are inversely related

• As one goes up the other goes down.

High frequency, Short Wavelength

Low frequency, Long Wavelength

Wave Formula

• All electromagnetic waves, including visible light, travel at the speed of 3.00 x 10 8 m/s in a vacuum.

• Speed of light = c = 3.00 x 108 m/s

c=fSpeed of light = (wavelength) x (frequency)

Example Problem

• What is the wavelength of a microwave having a frequency of 3.44 x 109 Hz?

Formula: c=f = ?f = 3.44 x 109 Hzc = 3.00 x 108 m/s

3.00 x 108 m/s = (3.44 x 109 s-1)3.00E8 / 3.44E9 = 8.72 x 10-2 m

Practice

• What is the frequency of green light, which has a wavelength of 5.90 x 10-7m?

• A popular radio station broadcast with a frequency of 94.7MHz, what is the wavelength of the broadcast? ( frequency needs to be is Hz)

• Different frequencies produce different types of waves.

• The entire range of frequencies is called the electromagnetic spectrum

• We are only able to see with our eyes a small portion of the spectrum = visible light

• ROY G BIV• Different colors mean different

frequencies/wavelengths

Energy & The Spectrum

• The energy of a wave increases with increasing frequency

• High Frequency = High Energy• Low Frequency = Low Energy• Blue light has more energy than Red light

Low energy

High energy

Low Frequency

High Frequency

Long Wavelength

Short Wavelength

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

GammaRays

Visible Light

Quanta

• Max Planck suggested the idea of quanta or packets of energy.

• Quanta is the minimum amount of energy that can be lost or gained by an atom.

• Energy is quantized = it comes in packets (like stairs or pennies only whole numbers)

Planck’s Constant

• h = 6.626 x 10-34 J.s (Joule seconds)Energy = (Planck’s constant)(frequency)

E = h fExample: What is the energy in Joules of a photon from the violet

portion of the rainbow if it has a frequency of 7.23 x 1014 Hz?E = ?h = 6.626 x 10-34 Jsf = 7.23 x 1014 Hz (or s-1)

E = (6.626 x 10-34 Js)(7.23 x 1014 s-1) E = 4.79 x 10-19 J

Photoelectric Effect• In the 1900s, scientist studied interactions of

light and matter.• One experiment involved the photoelectric

effect, which refers to the emission of electrons from a metal when light shines on the metal.

• This involved the frequency of the light. It was found that light was a form of energy that could knock an electron loose from a metal.

Photon

• Light waves can also be thought of as streams of particle.

• Einstein called these particles photons (He won a Nobel Prize for this)

• A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum energy.

Bohr’s Model

• Why don’t electrons fall into nucleus?

• Bohr suggested that they move like planets around sun.

• Certain amounts of energy separate one level from another.

• Nucleus is found inside a blurry “electron cloud”

Bohr’s Model

Nucleus

Electron

Orbit

Energy Levels

Bohr’s Model• Further away

from nucleus means more energy.

• There is no “in between” energy

• Energy LevelsIncr

easi

ng e

nerg

y

Nucleus

First

Second

Third

Fourth

Fifth

}

Bohr Model of the Atom• Ground state- the lowest energy state of an

atom.• Excited state – state in which an atom has a

higher potential energy than its ground state.• Energy is quantized. It comes in chunks.• quanta - amount of energy needed to move from

one energy level to another.• Since energy of an atom is never “in between”

there must be a quantum leap in energy.

Bohr Energy Levels

• K = 2 electrons – 1st• L = 8 electrons – 2nd• M = 18 electrons – 3rd• N = 32 electrons – 4th

Heisenberg Uncertainty Principle

• This is the theory that states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

Quantum Theory• Schrodinger derived an equation that

described energy & position of electrons in atom

• Schrodinger along with other scientists laid the foundation for the modern quantum theory, which describes mathematically the wave properties of electrons and other very small particles.