VISUAL PHYSICS ONLINE

7.1 NATURE OF LIGHT

ELECTROMAGNETIC WAVES (RADIATION)

P71 1906

(A) What is a blackbody?

(B) What is Wien’s Displacement Law?

(C) What is the significance of Wien’s Displacement Law?

(D) Give two examples of its use.

(E) Draw a graph which describes Wien’s Displacement Law. What do you need to

plot, to give a straight line graph?

View solution below only after you have completed answering the question. The solution is not in a form that you would answer in an examination. The answers are often in more detail to help improve your appreciation and understanding of the physics.

Solution

(A)

All objects with a temperature above absolute zero (0 K) emit energy in the form of electromagnetic radiation. A blackbody is an idealized object which absorbs all radiation falling on it, reflecting or transmitting none. It is a is a “perfect” absorber and a “perfect” emitter of radiation over all wavelengths.

(B)

Wien's displacement law: the blackbody radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The peak wavelength radiated from a blackbody moves to shorter towards wavelengths as the temperature T increases.

(C)

Wien's displacement law is relevant to many everyday experiences. By measuring the peak wavelength emitted by a hot object, you can estimate its surface temperature.

(D)

A piece of metal at room temperature emits mainly infrared wavelengths, which are not visible to our eyes. When the metal is heated, it first becomes “red hot” as the very longest visible wavelengths appear red. It then becomes more orange-red as the temperature is increased, and at very high temperatures would be described as "white hot" as shorter and shorter wavelengths come to predominate the black body emission spectrum.

One easily observes changes in the colour of an incandescent light bulb as the temperature of its filament is varied by a light dimmer. As the light is dimmed and the filament temperature decreases, the distribution of colour shifts toward longer wavelengths and the light appears redder, as well as dimmer.

A wood fire at 1500 K puts out peak radiation at about 2000 nm. 98% of its radiation is at wavelengths longer than 1000 nm, and only a tiny proportion at visible wavelengths (390–750 nm). Consequently, a campfire can keep one warm but is a poor source of visible light.

The colour of a star is used to determined its temperature from the Wien's law. In the constellation of Orion, one can compare Betelgeuse (T ≈ 3 300 K), Rigel (T = 12 100 K,), Bellatrix (T = 22 000 K), and Mintaka (T = 31800 K).

The preponderance of emission in the visible range, however, is not the case in most stars. The hot supergiant Rigel emits 60% of its light in the ultraviolet, while the cool supergiant Betelgeuse emits 85% of its light at infrared wavelengths. With both stars prominent in the constellation of Orion, one can easily appreciate the color difference between the blue-white Rigel (T = 12100 K) and the red Betelgeuse (T ≈ 3300 K). While few stars are as hot as Rigel, stars cooler than the Sun or even as cool as Betelgeuse are very commonplace.

Blackbody spectrum for a blue star at 7000 K

Mammals with a skin temperature of about 300 K emit peak radiation at around 10 μm (10 000 nm) in the far infrared. This is therefore the range of infrared wavelengths that pit viper snakes and infrared cameras must sense.

(E)