I. Waves & Particles

Ch. 4 - Electrons in Atoms

Light and Electrons

Because light and electrons have common properties,

understanding one helps to understand the other.

Electromagnetic radiation

Energy that exhibits wave-like behavior as it travels

Includes: gamma rays, X-rays, infrared, visible spectrum, microwaves, ultraviolet rays, radio and TV waves

EM Spectrum

LOW

ENERGY

HIGH

ENERGY

EM Spectrum

LOW

ENERGY

HIGH

ENERGY

R O Y G. B I V

red orange yellow green blue indigo violet

Waves

Wavelength () - length of one complete wave (measured in m, cm, nm)

Frequency () - # of waves that pass a point during a certain time period hertz (Hz) = 1/s (s-1)

Amplitude (A) - distance from the origin to the trough or crest

Waves

Agreater

amplitude

(intensity)

greater frequency

(color)

crest

origin

trough

A

EM Spectrum

Frequency & wavelength are inversely proportional

c = c: speed of light (3.00 108 m/s): wavelength (m, nm, etc.): frequency (Hz)

EM Spectrum

GIVEN:

= 7.50 x !012 Hz

= ?

c = 3.00 108 m/s

WORK:

= c

= 3.00 108 m/s 7.50 1012 Hz

= 4.00 10-5 m

EX: Calculate the wavelength of radiation whose frequency is 7.50 x !012 Hz.

Light as Particles

A property which could not be explained in terms of waves was a phenomenon known as the photoelectric effect – refers to the emission of electrons from a metal when heated or lit.

Quantum Theory

Planck (1900)

Observed - emission of light from hot objects

Concluded - energy is emitted in small, specific amounts (quanta)

Quantum - minimum amount of energy change

Quantum Theory

Planck (1900)

vs.

Classical Theory Quantum Theory

Quantum Theory

E: energy (J, joules)h: Planck’s constant (6.6262 10-34 J·s): frequency (Hz)

E = h

The energy of a photon is proportional to its frequency.

Quantum Theory

GIVEN:

E = ? = 3.55 1017 Hzh = 6.6262 10-34 J·s

WORK:

E = h

E = (6.6262 10-34 J·s)(3.55 1017 Hz)

E = 2.35 10-16 J

EX: Find the energy of a photon with a frequency of 3.55 1017 Hz.

Quantum Theory

Einstein (1905)

Observed - photoelectric effect

Quantum Theory

Einstein (1905)

Concluded - light has properties of both waves and particles

“wave-particle duality”

Photon - particle of light, having zero mass, carrying a quantum of energy

Quantum Theory

Radiation is emitted and absorbed only in whole

numbers of photons

II. Bohr Model of the Atom

Ch. 4 - Electrons in Atoms

A. Line-Emission Spectrum

ground state

excited state

ENERGY IN PHOTON OUT

B. Bohr Model

Linked the atom’s electron with photon emissione- exist only in paths, or orbits, with specific

amounts of energy called energy levels

Therefore…

e- can only gain or lose certain amounts of energy

only certain photons are produced

B. Bohr Model

1

23

456 Energy of photon depends on the difference in energy levels

e- jumps up when energy is absorbed-gives off light when is falls back down

C. Other Elements

Each element has a unique bright-line emission spectrum.

“Atomic Fingerprint”

Helium

Bohr’s calculations only worked for hydrogen!

Bohr’s model of the atom explained

electrons as

particles.

A. Electrons as Waves

Louis de Broglie (1924)

Applied wave-particle theory to e-

e- exhibit wave properties

B. Quantum Mechanics

Heisenberg Uncertainty Principle

Impossible to know both the velocity and position of an electron at the same time

B. Quantum Mechanics

σ3/2 Zπ

11s 0

eΨ a

Schrödinger Wave Equation (1926) treated e- moving around the nucleus as

waves

defines probability of finding an e-

defines mathematically the wave properties of electrons

B. Quantum Mechanics

Radial Distribution CurveOrbital

Orbital (“electron cloud”)

Region in space where there is 90% probability of finding an e-