Lecture 16: Electromanetic

Radiation• Reading: Zumdahl 12.1, 12.2

• Outline– The nature of electromagnetic radiation.

– Light as energy.– The workfunction of metals.

Electromagnetic Radiation

• Electromagnetic radiation or “light” is a form of energy.

• Characterized by:–Wavelength ()–Amplitude (A)

• Has both electric (E) and magnetic (H) components.

Electromagnetic Radiation (cont.)

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Electromagnetic Radiation (cont.)

• Wavelength (): The distance between two consecutive peaks in the wave.

Increasing Wavelength

1 > 2 > 3

Unit: length (m)

Electromagnetic Radiation (cont.)

• Frequency (): The number of waves (or cycles) that pass a given point in space per second.

Decreasing Frequency

1 < 2 < 3

Units: 1/time (1/sec)

Electromagnetic Radiation (cont.)

• The product of wavelength () and frequency () is a constant.

()() = c

Speed of light

c = 3 x 108 m/s

Electromagnetic Radiation (cont.)

• We classify electromagnetic radiation by wavelength.

• Visible radiation takes up only a small part of the electromagnetic spectrum.

Light as Energy

• Before 1900, it was assumed that energy and matter were not the same.

• The interaction of light with matter was one of the first examples where the separation of energy and matter fell apart.

Light as Energy (cont.)

• Planck’s experiments on light emitted from a solid heated to “incandescence”.

As body is heated, intensity increases, and peak wavelength shifts to smaller wavelengths.

Can “classical” physics reproduce this observation?

Light as Energy (cont.)

• Comparison of experiment to the “classical” prediction:

Classical prediction isfor significantly higherintensity as smaller wavelengths than what is observed.

“The Ultraviolet Catastrophe”

Light as Energy (cont.)

• Planck found that in order to model this behavior, one has to envision that energy (in the form of light) is lost in integer values according to:

E = nh

Energy Change

n = 1, 2, 3 (integers)

frequency

h = Planck’s constant = 6.626 x 10-34 J.s

Light as Energy (cont.)

• In general the relationship between frequency and “photon” energy is

Ephoton = h

• Example: What is the energy of a 500 nm photon?

= c/ = (3x108 m/s)/(5.0 x 10-7 m)

= 6 x 1014 1/s

E = h =(6.626 x 10-34 J.s)(6 x 1014 1/s) = 4 x 10-19 J

Waves vs. Particles• We began our discussion by defining light in terms of wave-like properties.

• But Planck’s relationships suggest that light can be thought of as a series of energy “packets” or photons.

The Photoelectric Effect

• Shine light on a metal and observe electrons that are released.

• Find that one needs a minimum amount of photon energy to see electrons (“o”).

• Also find that for ≥ o, number of electrons increases linearly with light intensity .

metal

The Photoelectric Effect (cont.)

The Photoelectric Effect (cont.)

• Finally, notice that as frequency of incident light is increased, kinetic energy of emitted e-

increases linearly.

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1

2meν

2 = hν photon −Φ

= energy needed to release e-

• Light apparently behaves as a particle.

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(Frequency )

The Photoelectric Effect (cont.)

• For Na with = 4.4 x 10-19 J, what wavelength corresponds to o?

€

1

2meν

2 = hν photon −Φ0

h = = 4.4 x 10-19 J

hc = 4.4 x 10-19 J

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=hc

4.4x10−19J=6.626x10−34 J.s( ) 3x10

8m /s( )

4.4x10−19J( )

= 4.52 x 10-7 m = 452 nm

00

(Frequency )

Interference of Light

• Shine light through a crystal and look at pattern of scattering.

• Diffraction can only be explained by treating light as a wave instead of a particle.

Summary• We have seen experimental examples where

light behaves both as a particle and as a wave.• This is referred to as “wave-particle” duality.

• Wave-particle duality is not limited to light! All matter demonstrates this behavior.

• Need something more than classical physics to describe such behavior….quantum mechanics!