Chapter 27 Quantum Physics

27.1 Blackbody Radiation and Planck’s Hypothesis

• An object at any temperature is known to emit radiation (electromagnetic waves) that is referred to as thermal radiation.

• Figure 27-2 (blackbody radiation curves)

a. At a given temperature, the intensity of the electromagnetic waves emitted by an object has a broad peak in a certain wavelength.

b. At higher temperature, the peak shifts to lower wavelength.

• Our sun (with surface temperature of ~6000 K) emits mostly yellow and our body (at 310 K), emits infrared (IR) waves.

• Wien’s displacement law describes the blackbody radiation curves

T = constant (0.2898 x 10^-2 m-K)

where is the wavelength at which the curve peaks and T is the absolute temperature of the object.

• In 1900 Max Planck calculated the blackbody radiation using a model, and that could fit the blackbody radiation curves.

• His model assumed that blackbody radiation was produced by submicroscopic oscillators (called resonators).

• Planck’s two assumptions;

1. The resonators could have only certain discrete amounts of energy (the quantization of the energy) given by

E_n = n h f n = 0, 1, 2, 3, …

where n is a positive integer, f is the frequency of vibration, and h is Planck’s constant (6.626 x 10^-34 J-s)

2. The resonators emit discrete units of light energy that is called photons. The resonators emit or absorb photons by “jumping” from one quantum state to another.

• Examples

27.2 The Photoelectric Effect

• The photoelectric effect is the phenomenon in which light shining on a metal surface causes electrons to be ejected from the surface. (Figure 27.4) Because the electrons are ejected with the aid of light, they are called photoelectrons.

• Figure 27.5 (Photoelectric current versus applied voltage) and Figure 27.6

When the applied voltage is less than (the stopping potential), no current.

• Several features of the photoelectric effect cannot be explained with classical physics or with the wave theory of light;

1. No electrons are emitted if the incident light frequency is below some cutoff frequency, f_c.

2. The maximum kinetic energy of the photoelectron is independent of light intensity.

3. The maximum kinetic energy of the photoelectron increases with increasing light frequency.

4. There is no delay of photoelectric effect.

• In 1905 Einstein presented an explanation of the photoelectric effect based on Planck’s work on quantized energy (photons).

KE_max = h f -

where h f is the photon energy, KE_max is the maximum kinetic energy of ejected electrons, and ( = h f_c) is the minimum work needed to eject electrons (the work function).

• When KE_max = 0, the energy of the incident photon (h f_c) is equal to the work function of the metal.

• Example

27.3 Applications of the Photoelectric Effect

27.4 X-Rays

• X-rays are electromagnetic waves emitted when high-energy electrons strike a metal target contained within an evacuated glass tube. (similar to an inverse photoelectric effect)

• Figure 27.10

• The emitted X-ray spectrum consists of sharp “peaks” or “lines”, called characteristic X-rays, superimposed on a broad continuous range of wavelengths called Bremsstrahlung. (Figure 27.11)

where is the energy of the electron after it has been accelerated through a potential difference of and the shortest wavelength produced by the process is .

• Examples

27.5 Diffraction of X-Rays by Crystals

• Similar to the diffraction of light by a multiple slit

27.6 The Compton Effect

• The Compton effect is the scattering of a photon by an electron in a material, the scattered photon having a smaller frequency than the incident photon. (Figure 27.17)

• The photoelectric effect and the Compton effect provide compelling evidence that light can exhibit particle-like characteristics attributable to energy packets called photons. (The same concept used in Planck’s assumptions.)

27.7 Pair Production and Annihilation

27.8 Photons and Electromagnetic Waves

• Physicists now believes that this wave-particle duality is an inherent property of light.

• Energy of a photon: E =

• Momentum of photon:

27.8 The Wave Properties of Particles

• In 1923, Louis de Broglie suggested that particles of matter should exhibit wave-like behavior. The wavelength of a particle () is given by

=

where h is Planck’s constant and p is the magnitude of the relativistic momentum of the particle.

• Examples

• Waves (light) can exhibit particle-like characteristics, and particles (electrons) can exhibit wave like characteristics.

< Application: The Electron Microscope >

• Figure 27.20 (Transmission Electron Microscope)

27.10 The Wave Function

• Each particle is represented by a wave function.

27.11 The Uncertainty Principle

• The Heisenberg uncertainty principle places limits on our knowledge about the behavior of a particle.

• Momentum and position

(p_x) (y)

where y = uncertainty in a particle’s position along the y-direction; p_x = uncertainty in the y component of the linear momentum of the particle.

• Energy and time

(E) (t)

where E = uncertainty in the energy of a particle when the particle is in a certain state; t = time interval during which the particle is in the state.

• Examples

27.12 The Scanning Tunneling Microscope