Quantum Theory

Waves Behave Like ParticlesMaxwell’s Wave Theory (1860)

Maxwell postulated that changing electric fields produce changing magnetic fields: EMradiation ~ EM waves.Discrepancy:1. The wave theory could not explain the spectrum

of light emitted by a hot body.2. It could not explain the photoelectric effect

Quantum Theory• Hot body – any body that has a temperature > 0

Kelvin Radiation From Incandescent BodiesLight & infrared radiation are produced by thevibration of the charged particles within theatom of a body that is so hot, it glows.• The higher the temperature, the more radiation at

frequencies of yellow, green, blue and violet is produced, and the “whiter” the body appears.

• The color you see depends on the relative amounts of emission at various frequencies.

Quantum Theory• (see Blackbody curve

http://cwx.prenhall.com/petrucci/medialib/media_portfolio/text_images/FG09_11.JPG)

• The higher the Kelvin temperature, the more intense the radiation is, and the higher the frequency that can be emitted.

Intensity – amount of energy emitted each second. (power)

The amount of energy emitted each second in EM waves is proportional to absolute temperature

raised to the 4th power (T4)** Maxwell could not explain the shape of a

blackbody curve**

Quantum TheoryMax Planck (1858-1947) – calculated the

spectrum (curve) – plot of radiation emitted at various frequencies.

Planck assumed the energy of vibration ofatoms could only have specific frequencies:E = n h f n = whole number

h = Planck’s constantf = frequencyE = Energy

Quantum Theory

This behavior is described as being quantized – energy only comes in packets of specific sizes.

Planck also stated: • Atoms could only emit radiation when their

vibration energy changed• Planck’s constant: h= 6.626 x 10 –34 J/Hz

The Photoelectric Effect

Maxwell could not explain why UV light discharged a negatively charged plate, but ordinary light could not.1905 – Albert Einstein explained the Photoelectric

Effect: Light & other forms of radiation consist of discrete bundles of energy called PHOTONS (particles of light). Each photon depends on the frequency of light.

The Photoelectric Effect

Energy of a Photon: E = h f

Dual Nature of Light

• Maxwell & Planck’s work proposed light and hot bodies’ wave nature

• Einstein proposed that light and other energy acted like particles

The Photoelectric Effect

Threshold frequency

• Electrons are only ejected if the frequency of the radiation is above a certain minimum value ~ threshold frequency (f0)

• This frequency varies with the type of metal (cathode) – only high frequency radiation ejects electrons.

The Photoelectric EffectEinstein’s Photoelectric EquationKE = h f - h f0 Restatement of the conservation of Energy

A photon with minimum energy (h f0 ) is needed to eject an electron.

Work Function (W0) – energy needed to free an electron from a metal. W0 = h f0

• Radiation with a frequency greater than the threshold frequency (f0 ) has more energy. The excess ( h f - h f0 ) becomes KE.

The Photoelectric Effect

The Kinetic Energy of the electrons can be determined by measuring the potential difference needed to stop them.

Work = KE = - q V0 V0 = stopping potential

The unit, Joule is too large for atomic systems so we use the electronvolt (eV)

1 eV = (1.6 x 10 -19 C) (1V) = 1.6 x 10 -19 CV

The Photoelectric Effect

Kinetic Energy vs. Frequency

KEmax slope = Planck’s constant

Frequency

The rate of photoemission (emitted e-) depends on

the intensity (power) of the incident light.

The Photoelectric Effect

Doubling the illumination (or intensity)

doubles the number of electrons emitted:

Photoelectric

Current

Intensity

The Photoelectric Effect

The maximum KE depends only on the

frequency of the incident radiation

(KE = hf – hf0).

KEmax

Intensity

KEmax is independent of the intensity of the light source.

The Compton Effect

Einstein predicted that a photon (even with no mass) has kinetic energy as a particle does, and Momentum, another particle property.

Recall: The photoelectric effect showed that photons have KE.

p = hf = h

c λ

The Compton Effect

Arthur Compton (1922) tested Einstein’s theory:

Compton Effect – the increase in λ when X-rays are scattered off of electrons

Result: A shift in energy

The Experiment: He directed X-rays at a graphite target and measured the λ’s of the scattered X-rays

The Compton Effect

E = hc E = hf where f = c/λ λ**increased wavelength meant that both energy &

momentum were lost by the photon**-the incoming photon suffers an elastic collision with

an atomic electronEnergy & momentum are transferred to the electron

**this is another proof of light’s particle behavior**

The Compton Effect

Incoming photon e-

e-

outgoing photon

increased λ

Particles Behave like Waves

• Photoelectric Effect

• Compton Scattering

1923 Louis Victor de Broglie

• Suggested particles have wave properties

Showed particle nature

Matter Waves

Recall: p = mv and momentum of a photon:p = h/λ

So… p = mv = h/λRewrite the equation:λ = h/p = h/mv de Broglie wavelength• de Broglie suggested that all matter has wave

properties • The de Broglie wavelength for ordinary matter

(macroscopic) is far too small to produce observable effects

Matter Waves

Particles & Waves

EM waves show particle-like properties:

Photoelectric Effect & Compton Effect

Particles show wave-like properties:

Diffraction & Interference

The Atom

Rutherford & the Nuclear Model(previously, J.J.Thompson discovered the

electron & he believed a massive, positively

charged substance was also in the

atom~arranged like raisins in a muffin)

Ernest Rutherford proved otherwise…

Rutherford’s Experiment• He directed a beam of alpha particles at a thin

sheet of gold foil (only a few atoms thick)• (an alpha particle is a helium nucleus consisting of

2 protons & 2 neutrons)• He noticed the following: ALPHA PARTICLE

SCATTERING…

The Atom

Alpha particle scattering:

1. Most passed through undeflected

2. Some(small percentage) are scattered through angles ranging up to 180°. They are hyperbolic paths because of electric forces (Coulomb forces) between the particles and the positive nuclei

3. Some completely rebounded

The Atom

• Rutherford explained these results by using Coulomb’s law and Newton’s laws of motion:– All positive charge of the atom is concentrated

at the nucleus– All mass is in the nucleus (99%)– Electrons are outside and far away from the

nucleus

NUCLEAR MODEL

The Atom

Nuclear Model Limitations:

1. It did not account for the lack of emission of radiation as electrons move around the nucleus

2. It did not account for the spectrum of each element

The Atom

The Bohr Model of the Atom

Many physicists tried to explain the atomic

spectra of various elements.

Niels Bohr (Danish Physicist)

• Tried to unite Rutherford’s model with Einstein’s theory of light (photons with discrete energy) PLANETARY MODEL

The Atom

Bohr Model:1. The electron can only travel around the nucleus

in certain select orbits and no others.2. An electron may exist only in these orbits where

its angular momentum (mvr) is an integral multiple of Planck’s constant divided by 2

3. When an electron changes from one energy state to another, a quantum of energy equal to the difference between the energies of two states is emitted or absorbed.

The Atom

The change in energy is given by:

hf = Ei – Ef Ei = energy of the initial

state

Ef = energy of the final

state

The photon must be exactly large enough (quantized) to raise

or lower the electron to another allowable orbit. Otherwise

the atom cannot absorb or emit it.

The Atom

n = 3

n = 2

n = 1

Photon emittedhf = E3 – E2

f = E3 – E2

h

Atomic Spectra

• The arrangement of electrons around the nucleus can be predicted by the EMISSION SPECTRA.

EMISSION SPECTRA – set of visible wavelengths emitted by an atom

• The properties of individual atoms only becomes apparent when they are not combined with other elements.

(recall: an incandescent blackbody’s spectrum does not depend on the type of atom that makes its up)

You can see an emission spectrum of a type of atom by looking through a diffraction grating or by putting the grating in front of a lens.

Spectrascope – light passes through a slit, then is dispersed by passing through a prism- each forms an image on the slit(dispersion)

Atomic Spectra

Spectrum tubes (gas discharge tubes) – the gas glows when HIGH VOLTAGE is applied. The electrons collide and transfer energy to the atoms ~ the atoms give up this energy in the form of EM radiation

Incandescent solids – show a continuous spectrumGases – show a series of lines of different colors,

each a Analysis of line Spectra• Can tell us what elements are present• The relative amounts of the elements

Atomic Spectra

• By comparing intensities of lines, percentages of compositions can be determined

ABSORPTION SPECTRA

• Gases will absorb light at characteristic wavelengths when they are cooled (reverse of emission)

Atomic Spectra

• White light is sent through a sample of gas and through a spectrascope

• What normally would be a continuous spectrum now has dark lines in it.

• Bright lines of an emission spectra and dark lines of an absorption spectra occur at the same .

Analysis of spectra allows for the identification of the elements that make up a mixture

Fraunhofer – noticed some dark lines while examining the sun – Fraunhofer lines.

Atomic Spectra