Quantum Theory of the Atom

Chapter 7

Dr. Victor Vilchiz

Light an Important Tool

• Light was a great tool that aided the discovery of the structure of the atoms.

• It is fitting that before we discuss how exactly atoms are composed and the models that have been developed that we talk about light.

• As we will see Light can be described both as a particle or as a wave… lets start with the wave description.

The Wave Nature of Light

• A wave is a continuously repeating change or oscillation in matter or in a physical field. Light is also a wave.

It consists of oscillations in electric and magnetic fields that travel through space.

Visible light, X rays, and radio waves are all forms of electromagnetic radiation.

The electromagnetic spectrum.

The Wave Nature of Light

• A wave can be characterized by its wavelength and frequency.The wavelength, lambda), is the distance between any two adjacent identical points of a wave and it is usually associated with the color of the radiation. (see Figure 7.3)

The frequency, (nu), of a wave is the number of wavelengths that pass a fixed point in one second.

The amplitude is often confused as been a characteristic of the wave but it is not.

So, given the frequency of light, its wavelength can be calculated, or vice versa.

The Wave Nature of Light

• The product of the frequency, (waves/sec) and the wavelength, (m/wave) would give the speed of the wave in m/s.

In a vacuum, the speed of light, c, is 3.00 x 108 m/s. Therefore,

c

If c = then rearranging, we obtain = c/

The Wave Nature of Light

• What is the wavelength of yellow light with a frequency of 5.09 x 1014 s-1? (Note: s-1, commonly referred to as Hertz (Hz) is defined as “cycles or waves per second”.)

nm 589or m1089.5 7s10 09.5

)s/m10 00.3(114

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If c = then rearranging, we obtain = c/

The Wave Nature of Light

• What is the frequency of violet light with a wavelength of 408 nm? (see Figure 7.5)

114m10 408

s/m10 00.3 s1035.79

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The limits of Visible light depend on how good your vision might be but they are located on the violet end at about 400 nm and on the red end at about 800 nm.

Beyond these extremes, electromagnetic radiation is not visible to the human eye.

The Wave Nature of Light

• The range of frequencies or wavelengths of electromagnetic radiation is called the electromagnetic spectrum. (see Figure 7.5)

Wave or Particle?

• The biggest question to arise in the early 1900’s was regarding the fundamental nature of light. Is light made out of waves or particles?

• Many experiments were done in the process of developing what we now call Quantum Theory from Classical Theory and

Black Body Radiation

• In 1900 Max Planck noticed that if certain “black bodies” were heated they will start glowing.– Blackbody radiation.

• At 1000K it gives a red glow• At 1500K it is orange• At 2000K it is white (all colors)

– If the radiation was to follow classical theory there should be a gradual change of colors through the spectrum.

Birth of Quantum Theory

• Planck’s Quantization of EnergyAs an explanation to the results of the blackbody radiation experiment Planck proposes that the atoms of a solid oscillate with a definite frequency, He went on to introduce the first notion of quantization by proposing that an atom could have only certain energies of vibration, E, those allowed by the formula

where n must be an integer (not zero) and h (Planck’s constant) is assigned a value of 6.63 x 10-34 J. s.

nhE

Quantum Effects and Photons

• Planck’s Quantization of Energy.Thus, the only energies a vibrating atom can have are h, 2h, 3h, and so forth.

The numbers symbolized by n are now called quantum numbers.

Therefore the vibrational energies of the atoms are said to be quantized.

Photoelectric Effect

• Planck’s conclusions and proposals were not well received by the scientific community since they challenged theories that were well accepted. Among his critics was a world renown physicist, Albert Einstein.

While Einstein publicly rejected the conclusions of Planck, he started experiments of his own to try to find flaws on the new theory.

In 1905, Albert Einstein proposed that light had both wave and particle properties as observed in the photoelectric effect. (see Figure 7.6)

Photoelectric Effect

• Photoelectric EffectEinstein extended Planck’s work to include the structure of light itself.• If a vibrating atom changed energy from 3h

to 2h, it would decrease in energy by h.

• He proposed that this energy would be emitted as a bit (or quantum) of light energy.

• Einstein postulated that these “bits” were the fundamental components of light. Those “bits” are now called photons and are considered particles of electromagnetic energy.