College Physics

Planck’s constant:

particle-wave duality:

photoelectric effect:

photon energy:

photon momentum:

photon:

probability distribution:

quantized:

quantum mechanics:

ultraviolet radiation:

uncertainty in energy:

uncertainty in momentum:

uncertainty in position:

uncertainty in time:

visible light:

x ray:

h= 6.626×10

–34

J ⋅ s

the property of behaving like either a particle or a wave; the term for the phenomenon that all particles have wave characteristics

the phenomenon whereby some materials eject electrons when light is shined on them

the amount of energy a photon has;E=hf

the amount of momentum a photon has, calculated by p=h

λ

=Ec

a quantum, or particle, of electromagnetic radiation

the overall spatial distribution of probabilities to find a particle at a given location

the fact that certain physical entities exist only with particular discrete values and not every conceivable value

the branch of physics that deals with small objects and with the quantization of various entities, especially energy

UV; ionizing photons slightly more energetic than violet light

lack of precision or lack of knowledge of precise results in measurements of energy

lack of precision or lack of knowledge of precise results in measurements of momentum

lack of precision or lack of knowledge of precise results in measurements of position

lack of precision or lack of knowledge of precise results in measurements of time

the range of photon energies the human eye can detect

EM photon betweenγ-ray and UV in energy

Section Summary

29.1 Quantization of Energy

The first indication that energy is sometimes quantized came from blackbody radiation, which is the emission of EM radiation by an object with
an emissivity of 1.

• Planck recognized that the energy levels of the emitting atoms and molecules were quantized, with only the allowed values ofE=

⎛

⎝n+

1

2

⎞

⎠hf,

wherenis any non-negative integer (0, 1, 2, 3, ...).

• his Planck’s constant, whose value ish= 6.626×10

–34

J ⋅ s.

Thus, the oscillatory absorption and emission energies of atoms and molecules in a blackbody could increase or decrease only in steps of size

ΔE=hfwhere fis the frequency of the oscillatory nature of the absorption and emission of EM radiation.

Another indication of energy levels being quantized in atoms and molecules comes from the lines in atomic spectra, which are the EM
emissions of individual atoms and molecules.

29.2 The Photoelectric Effect

The photoelectric effect is the process in which EM radiation ejects electrons from a material.

• Einstein proposed photons to be quanta of EM radiation having energyE=hf, where f is the frequency of the radiation.

All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of
individual photons with individual electrons.

• The maximum kinetic energyKEeof ejected electrons (photoelectrons) is given byKEe=hf– BE, wherehf is the photon energy and BE

is the binding energy (or work function) of the electron to the particular material.

29.3 Photon Energies and the Electromagnetic Spectrum

Photon energy is responsible for many characteristics of EM radiation, being particularly noticeable at high frequencies.

Photons have both wave and particle characteristics.

29.4 Photon Momentum

• Photons have momentum, given by p=h

λ

, whereλis the photon wavelength.

• Photon energy and momentum are related byp=Ec, whereE=hf=hc/λfor a photon.

29.5 The Particle-Wave Duality

EM radiation can behave like either a particle or a wave.

This is termed particle-wave duality.

1056 CHAPTER 29 | INTRODUCTION TO QUANTUM PHYSICS

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