Module 6

Module 6—Wave-Particle Duality and Quantum Physics

 

Explore

 

Blackbody Radiation

 

In 1862 German physicist Gustav Kirchhoff introduced the term blackbody to describe a hypothetical object that absorbs all of the electromagnetic radiation (EMR) that falls on it. In theory, the energy of all the absorbed EMR causes the blackbody to heat up and become a perfect radiator, emitting energy back to the environment in the form of EMR. Some of the EMR can be seen in red- or white-hot objects and longer wavelengths can be felt as heat. The heating element on a stove can be considered a blackbody radiator—you can feel the infrared EMR and see the visible EMR at sufficient temperatures.

 

The relationship between temperature and colour can be summarized using a Blackbody Spectrum simulation. Open the simulation and see what happens when you adjust the temperature using the slider.

 

As illustrated below, the simulation shows the observed colour of an object at the temperature indicated on the slider. In this example, a blackbody radiation curve shows the distribution of energy by wavelengths released by an incandescent light bulb when it is 3045 Kelvin (2772°C). Notice that the bulb emits most of its energy in wavelengths slightly larger than those of visible light, which is infrared heat. Interestingly, this is why an incandescent light bulb is very inefficient at producing light—90% of the energy it consumes produces infrared heat rather than visible light!

 

One interesting thing about blackbody radiation curves is that you can use an object’s curve, along with its observed colour, to tell the object’s temperature!

 

© The University of Colorado, under the GNU General Public License (GPL)

 

Try This

 

TR 1. Using the Blackbody Spectrum simulation, complete the third relationship between colour and temperature.

1. Extremely hot, glowing objects, such as stars, emit a continuous range of wavelengths, making them appear white.
   
   
2. At a given temperature, the energy emitted by a hot object comprises a specific range of wavelengths, giving it a unique colour.
   
   
3. At _______ temperatures, an object emits more blue light; at _______ temperatures, it emits more red light.
   

Self-Check

 

SC 1. Using the radiation curves in the simulation, explain why a light bulb appears white while an oven element only has a slight red glow. What does this imply about the temperature of the filament in a light bulb compared to that of an element in a stove?

 

 

Read

 

Read pages 704 and 705 of the textbook for more information on blackbody radiation and curves. Note that some of the radiation curves shown in the text are related to frequency rather than to wavelength, as seen in the simulation.

 

The Quantum

 

 

The explanation for blackbody radiation and, in particular, the shape of the radiation curves, could not be found in classical physics. For example, classical physics predicts that as an object heats up it should start releasing energy in shorter and shorter wavelengths, since this is the most efficient way to release energy. At very high temperatures, the amount of energy released is maximized by the release of ever-shorter wavelengths.

 

However, the blackbody radiation curves produced by hot objects show that even at extremely high temperatures, most of the energy is released by relatively long wavelengths with little or no energy released by very short wavelengths. The explanation for the shape of the observed curves came from Max Planck in the year 1900. He could account for the shape by assuming that there was a specific amount of energy that any given wavelength of radiation could exchange with its environment. The term quantum refers to this specific energy, and it is related to the wavelength of the radiation by Planck’s formula.

 

 

Planck’s EMR energy is the product of the number of quanta, Planck’s constant, and the frequency of the radiation

Quantity Symbol SI Unit quantum energy E J Planck’s constant h 6.63 × 10–34 J•s or 4.14 × 10–15 eV•s frequency f Hz or /s number of quanta* n no units

* n refers to the whole number of quanta that make up the total amount of energy (E) transferred by the radiation; therefore, n = 1, 2, 3, 4, . . . .

Note that Planck’s formula applies equally to wavelength as it is related to frequency by the universal wave equation.

 

Planck’s formula represents a fundamental shift in theory. In this system the amount of energy that can be exchanged between radiation and its surroundings is quantized, or limited to whole-number multiples of the smallest unit of energy—the quantum. Furthermore, the value of each quantum is equal to the product of Planck’s constant and the frequency of the radiation (E = hf). The concept of the quantum effectively ended classical physics and gave birth to quantum physics.

 

Several years later Albert Einstein proposed that radiation, including visible light, could be quantized regardless of whether or not it exchanges energy with its surroundings. In 1926 chemist Gilbert Lewis introduced the term photon to describe a single quantum of light. The energy of one photon is given from Planck’s formula and is E = hf.

 

Read

 

Read “Einstein, Quanta, and the Photon” on page 706 of the textbook.

 

Try This

 

TR 2. Complete “Practice Problems” 1, 2, and 3 on page 706 of the textbook.

 

TR 3. Complete “Practice Problems” 1, 2, and 3 on page 707 of the textbook.

 

TR 4. Complete “Practice Problems” 1 and 2 on page 708 of the textbook.

 

Energy and the Spectrum

 

Planck’s formula associates photon energy with the frequency of radiation, expanding the electromagnetic spectrum to show the energy of various classifications of EMR.

 

 

Module 6: Lesson 1 Assignment

 

Remember to submit your answers to A 1, A 2, A 3, A 4, A 5, A 6, A 7, and D 3 to your teacher as part of your Module 6: Lesson 1 Assignment.

 

A 1. Why couldn’t classical physics explain blackbody radiation curves?

A 2. What is the frequency of a 13.0-eV photon?

A 3. What is the wavelength of a 4.30×10–19-J photon?

A 4. How many photons with a wavelength of 532 nm are released each second by a 5.0-mW laser?

A 5. As a safety precaution when working with lasers, scientists wear red-coloured glasses that will block all colours but red. Why is a red laser safer than a blue laser?

A 6. A person lives near a 50-kW radio tower. Why is it safe to live near the high-power radio tower but dangerous to be exposed to an X-ray machine that uses 7.5 kW?

 

A 7. Why did the introduction of the photon effectively end classical physics? What does this mean for the Christiaan Huygens theory that light is a series of waves and Thomas Young’s double-slit experiment?

 

Discuss

 

D 1. Develop a mnemonic that will help you remember the order of radiation given in “Figure 14.6” on page 709 of the textbook. RMIVUXG = Radio Microwave Infrared Visible Ultraviolet X-ray Gamma. Post your mnemonic in the discussion area for your class.

 

 

 

D 3. Read the answers from two other students for D 2 and improve your own answer. Explain what you learned from reading the other students’ answers and if or how you changed your own solution.

 

 

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