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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-