Transcript Physics and the Quantum Mechanical Model

Connection
 The Quantum Mechanical Model grew out of the
study of light.
 Scientists originally believed light was a particle, just
like matter.
 However, by 1900, it was generally accepted that light
was a wave phenomenon.
 Light consisted of electromagnetic waves
Light
 Electromagnetic Radiation includes radio waves,
microwaves, infrared waves, visible light, ultraviolet
waves, x-rays, and gamma rays
 All light travels at 2.998 x 108 m/s, in a vacuum (absence
of matter)
Waves
 Electromagnetic waves (light) have the same structure
as your normal wave.
 Wavelength () is the distance between two consecutive
crests (or troughs) (unit => m or nm)
 Amplitude (A) is the height of a wave, or the distance from
the origin to the crest. (unit => m or nm)
 Frequency () is the number of wave cycles to pass a given
point per unit of time (unit => Hz or 1/s)
Equation
 Wavelength and Frequency have an inverse
relationship.
 They are related by the velocity or speed of light (c) –
see above
 The equation that relates frequency, wavelength, and
speed of light is:
 c=.
Spectra
 A spectrum is the range of wavelengths associated with
light.
 The electromagnetic spectrum gives the range of
wavelengths of all types of light.
 Visible white light produces the continuous spectrum that we
associate with the colors of the rainbow (ROY G BIV)
 However, not all light produces a continuous spectrum.
 When matter becomes electrically charged, it can begin to give off
light.
 The light given off by an element is called an Atomic Emission
Spectrum.
 This spectrum is discontinuous.
 It appears as a series of disconnected lines on the electromagnetic
spectrum.
Uses of Spectra
 Scientists use an Emission Spectrograph to analyze the
wavelengths of light given off by charged elements.
 The emission spectrograph gives the entire range of
wavelengths associated with the light from the element.
 Scientists have found that no two elements share the exact
same Atomic Emission Spectrum.
 The AES can be used like a fingerprint to determine the
types of element in a sample of matter
 Very useful in astronomy
 A spectroscope can be used to analyze the spectrum
found within the visible light range.
Quantum Concept and
Photoelectric Effect
 What we knew about energy said the spectra of
elements should be continuous because…
 There should be no limit to how small the Energy lost or
gained by an object can be.
 Max Planck attempted to explain the discrepancy
 Examined the color change of Iron as it is heated.

Explanation: Energy of a body changes in small
discrete units
E=h 
.
 So…The amount of radiant Energy (light) absorbed or
emitted is proportional to the frequency of the
radiation
 E   or E = h . 
 Planck calculated the value of the proportionality
constant
 Planck’s constant: h = 6.6262 x 10-34 J.s
E=h 
.
 This equation allowed scientists to determine the
value of a quantum.
 Because…when an electron moves from a higher energy
level to a lower energy level, it will emit energy in the
form of light. We can determine the wavelength and
frequency of the light emitted and use it to calculate the
energy associated with these electron transitions.
E=h 
.
 The energy calculated using Planck’s equation
equals the energy of a quantum.
 So…


Low-frequency radiation --- Small Energy change
High-frequency radiation --- Large Energy change
Einstein
 Einstein proposed that light could be described as
quanta of energy that behaved like particles
 Called them Photons
Energy of a Photon => E= h . 
 This Dual Wave-Particle Behavior of light explains the
Photoelectric Effect.

Photoelectric Effect
 Metals eject electrons called photoelectrons when
light shines on them.
 Alkali metals are the most susceptible.
 Not all wavelengths of light create this phenomenon
 The wavelength must have a threshold value of
energy (Ladder analogy)
 In monochromatic light, all photons have the
same Energy
 Solar cells use the photoelectric effect to produce
electricity.
Wavelength of a Particle
 Louis de Broglie wondered if particles of matter could
behave like waves
 If light could do both, why not matter…
 He developed an equation that predicted the wavelength of a
moving particle of matter
 = __h__
m.v




 = wavelength of a moving particle of matter
h = Planck’s constant
m = mass of particle
v = velocity of particle
Classical Mechanics vs.
Quantum Mechanics
 Quantum Theory created a split in the area of
mechanics. The quantum concept did not fit with
the traditional ideas about how matter and energy
behaved.
Classical Mechanics
 describes the motion of large bodies
 Therefore, it appears that the body can gain or lose
energy in any amount
Quantum Mechanics
 Describes the motion of subatomic particles and atoms as
waves
 Therefore, they gain or lose energy in packages called
quanta
 Includes the uncertainty principle
 Because these particles are extremely small, they are affected by
interactions with photons.
 Heisenberg’s uncertainty principle states that It is impossible to
know both the position and the velocity of a particle at the same
time.
 Only way to know precise position of a subatomic particle is for a
photon (light) to collide with it.
 The collision will change the velocity of the particle
 Therefore, we can’t know both at the exact same time.