Chapter 27Chapter 27

Quantum Physics

General Physics

Quantum Physics I

Sections 1–3

General Physics

Need for Quantum Physics

Other problems remained in classical physics which relativity did not explain

Blackbody Radiation– The electromagnetic radiation emitted by a heated object

Photoelectric Effect– Emission of electrons by an illuminated metal

Compton Effect– A beam of x-rays directed toward a block of graphite

scattered at a slightly longer wavelength Spectral Lines

– Emission of sharp spectral lines by gas atoms in an electric discharge tube

General Physics

Development of Quantum Physics

Beginning in 1900– Development of ideas of quantum physics

• Also called wave mechanics• Highly successful in explaining the behavior of atoms,

molecules, and nuclei

Involved a large number of physicists

General Physics

Particles vs. WavesPARTICLE properties

individual motion position(time) – localized velocity v = x / t mass energy, momentum dynamics: F=ma interaction – collisions

quantum states spin

WAVE properties

collective motion wavelength (freq) – periodic velocity v = f dispersion energy, momentum dynamics: wave equation interference – superposition reflection, refraction, trans. diffraction – Huygens standing waves – modes polarization

General Physics

Blackbody Radiation

An object at any temperature emits electromagnetic radiation– Sometimes called thermal radiation– Stefan’s Law describes the total power

radiated

– The spectrum of the radiation depends on the temperature and properties of the object

4TPower

General Physics

General Physics

General Physics

IR heat lamp Red hot Night vision

Silver heat shield Space blanket

General Physics

General Physics

General Physics

Blackbody Radiation Graph Experimental data for distribution of

energy in blackbody radiation As the temperature increases, the

total amount of energy increases– Shown by the area under the curve

As the temperature increases, the peak of the distribution shifts to shorter wavelengths

The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law– λmax T = 0.2898 x 10-2 m • K

• λmax is the wavelength at which the curve’s peak

• T is the absolute temperature of the object emitting the radiation

Active Figure: Blackbody Radiation

General Physics

The Ultraviolet Catastrophe

Classical theory did not match the experimental data

At long wavelengths, the match is good

At short wavelengths, classical theory predicted infinite energy

At short wavelengths, experiment showed no energy

This contradiction is called the ultraviolet catastrophe

General Physics

Max Planck

1858 – 1947 Introduced a “quantum

of action” now known as Planck’s constant

Awarded Nobel Prize in 1918 for discovering the quantized nature of energy

General Physics

Planck’s Resolution

Planck hypothesized that the blackbody radiation was produced by resonators– Resonators were submicroscopic charged oscillators

The resonators could only have discrete energies– En = n h ƒ

• n is called the quantum number• ƒ is the frequency of vibration• h is Planck’s constant, h = 6.626 x 10-34 J s

Key Point: quantized energy states Few high energy resonators populated

Active Figure: Planck's Quantized Energy States

General Physics

Photoelectric Effect

When light is incident on certain metallic surfaces, electrons are emitted from the surface– This is called the photoelectric effect– The emitted electrons are called photoelectrons

The effect was first discovered by Hertz The successful explanation of the effect was

given by Einstein in 1905– Received Nobel Prize in 1921 for paper on

electromagnetic radiation, of which the photoelectric effect was a part

General Physics

Photoelectric Effect Schematic When light strikes E, photoelectrons

are emitted Electrons collected at C and passing

through the ammeter are a current in the circuit

C is maintained at a positive potential by the power supply

The current increases with intensity, until reaching a saturation level

No current flows for voltages less than or equal to –ΔVs, the stopping potential

The maximum kinetic energy of the photoelectrons is related to the stopping potential: KEmax = eVs

Active Figure: The Photoelectric Effect

General Physics

Features Not Explained by Classical Physics/Wave Theory

The stopping potential Vs (maximum kinetic energy KEmax) is independent of the radiation intensity

Instead, the maximum kinetic energy KEmax of the photoelectrons depends on the light frequency

No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated

Electrons are emitted from the surface almost instantaneously, even at very low intensities

General Physics

Einstein’s Explanation A tiny wave packet of light energy, called a photon,

would be emitted when a quantized oscillator jumped from one energy level to the next lower one– Extended Planck’s idea of quantization to E.M. radiation

The photon’s energy would be E = hƒ

Each photon can give all its energy to an electron in the metal

The maximum kinetic energy of the liberated photoelectron is KEmax = hƒ –

is called the work function of the metal – it is the energy needed by the electron to escape the metal

General Physics

Explains Classical “Problems”

KEmax = hƒ – – The effect is not observed below a certain cutoff

frequency since the photon energy must be greater than or equal to the work function – without enough energy, electrons are not emitted, regardless of the intensity of the light

– The maximum KE depends only on the frequency and the work function, not on the intensity

– The maximum KE increases with increasing frequency

– The effect is instantaneous since there is a one-to-one interaction between the photon and the electron

General Physics

Verification of Einstein’s Theory

Experimental observations of a linear relationship between KEmax and frequency ƒ confirm Einstein’s theory

The x-intercept is the cutoff frequency– KEmax = 0 →

KEmax = hƒ –

hfc

General Physics

Cutoff Wavelength

The cutoff wavelength is related to the work function

Wavelengths greater than C incident on a material with a work function don’t result in the emission of photoelectrons

c

hc

General Physics

Photocells

Photocells are an application of the photoelectric effect

When light of sufficiently high frequency falls on the cell, a current is produced

Examples– Streetlights, garage door openers, elevators

General Physics

X-Rays

Electromagnetic radiation with short wavelengths– Wavelengths less than for ultraviolet– Wavelengths are typically about 0.1 nm– X-rays have the ability to penetrate most materials

with relative ease– High energy photons which can break chemical

bonds – danger to tissue

Discovered and named by Roentgen in 1895

General Physics

Production by an X-Ray Tube

X-rays are produced when high-speed electrons are suddenly slowed down

– Can be caused by the electron striking a metal target

A current in the filament causes electrons to be emitted

These freed electrons are accelerated toward a dense metal target

The target is held at a higher potential than the filament

General Physics

X-ray Tube Spectrum

The x-ray spectrum has two distinct components

Continuous broad spectrum– Depends on voltage applied to

the tube– Cutoff wavelength– Called bremsstrahlung

(“braking”) radiation The sharp, intense lines

depend on the nature of the target material

General Physics

An electron passes near a target nucleus

The electron is deflected from its path by its attraction to the nucleus– This produces an

acceleration It will emit

electromagnetic radiation when it is accelerated

Production of X-rays, 2

General Physics

Wavelengths Produced If the electron loses all of its energy in the

collision, the initial energy of the electron is completely transformed into a photon

The wavelength can be found from

Not all radiation produced is at this wavelength– Many electrons undergo more than one collision

before being stopped– This results in the continuous spectrum produced

maxmin

ƒhc

e V h

General Physics

Tumors usually have an irregular shape

Three-dimensional conformal radiation therapy (3D-CRT) uses sophisticated computers and CT scans and/or MRI scans to create detailed 3-D representations of the tumor and surrounding organs

Radiation beams are then shaped exactly to the size and shape of the tumor

Because the radiation beams are very precisely directed, nearby normal tissue receives less radiation exposure

X-ray Applications, X-ray Applications, Three-Dimensional Three-Dimensional Conformal Radiation Therapy (3D-Conformal Radiation Therapy (3D-

CRT)CRT)