Concept Summary

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Topic | Discussion | Learning Aids
Wave - particle duality | 29.1 THE WAVE-PARTICLE DUALITY, 29.2 BLACKBODY RADIATION AND PLANCK’s CONSTANT The Wave-Particle duality refers to the fact that a wave can exhibit particle-like characteristics and a particle can exhibit wave-like characteristics. |
Perfect blackbody | At a constant temperature, a perfect blackbody absorbs and reemits all the electromagnetic radiation that falls on it. Max Planck calculated the emitted radiation intensity per unit wavelength as a function of wavelength. In his theory, Planck assumed that a blackbody consists of atomic oscillators that can have only discrete, or quantized, energies. Planck’s quantized energies are given by |
Energies of atomic oscillators |

| (29.1)

where h is Planck’s constant () and f is the vibration frequency of an oscillator.
| 29.3 PHOTONS AND THE PHOTOELECTRIC EFFECT All electromagnetic radiation consists of photons, which are packets of energy. The energy of a photon is |
Energy of a photon |

| (29.2)

where h is Planck’s constant and f is the frequency of the photon. A photon has no mass and always travels at the speed of light c in a vacuum.
Photoelectric effect Work function | The photoelectric effect is the phenomenon in which light shining on a metal surface causes electrons to be ejected from the surface. The work function W0 of a metal is the minimum work that must be done to eject an electron from the metal. In accordance with the conservation of energy, the electrons ejected from a metal have a maximum kinetic energy KEmax that is related to the energy hf of the incident photon and the work function of the metal by |
Conservation of energy and the photoelectric effect |

| (29.3)

Use Self-Assessment Test 29.1 to evaluate your understanding of Sections 29.1, 29.2 and 29.3 .

Magnitude of a photon’s momentum | 29.4 THE MOMENTUM OF A PHOTON AND THE COMPTON EFFECT The magnitude p of a photon’s momentum is

| (29.6)

where h is Planck’s constant and is the wavelength of the photon.
Compton effect | The Compton effect is the scattering of a photon by an electron in a material, the scattered photon having a smaller frequency and, hence, a smaller energy than the incident photon. Part of the photon’s energy and momentum are transferred to the recoiling electron. The difference between the wavelength of the scattered photon and the wavelength of the incident photon is related to the scattering angle by |
Wavelength difference in the Compton effect |

| (29.7)

Compton wavelength of the electron | where m is the mass of the electron. The quantity h/(mc) is known as the Compton wavelength of the electron. |
| 29.5 THE DE BROGLIE WAVELENGTH AND THE WAVE NATURE OF MATTER The de Broglie wavelength of a particle is |
De Broglie wavelength |

| (29.8)

| where h is Planck’s constant and p is the magnitude of the relativistic momentum of the particle. Because of its wavelength, a particle can exhibit wave-like characteristics. The wave associated with a particle is a wave of probability. |
| 29.6 THE HEISENBERG UNCERTAINTY PRINCIPLE The Heisenberg uncertainty principle places limits on our knowledge about the behavior of a particle. The uncertainty principle indicates that |
Uncertainty principle–momentum and position |

| (29.10)

| where is the uncertainty in the particle’s position along the y direction, and is the uncertainty in the y-component of the linear momentum of the particle. The uncertainty principle also states that |
Uncertainty principle–energy and time |

| (29.11)

| where is the uncertainty in the energy of a particle when it is in a certain state, and is the time interval during which the particle is in the state. |

Use Self-Assessment Test 29.2 to evaluate your understanding of Sections 29.4, 29.5 and 29.6 .

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