Homework 6††† due Thursday, March 27

 

1.     Check out http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm.It is an applet which will plot a thermal radiation curve (also called a blackbody curve) for various temperatures.†† Make sure that ďAuto-XĒ and ďAuto-YĒ are not selected.What is the peak wavelength of the following objects, and what color do they appear?

a.      Sun (6000) K

Around 5000 Angstroms, according to the plot.The plot shows that the Sun would appear white or greenish.In fact, it looks yellow because of how our eyes work.

 

b.     Human body (98.6 F; convert to Kelvin); calculate lmax using Wienís law.

This is 310 K, and the plot shows the peak is somewhere in the infrared; i.e. at wavelengths greater than 10,000 Angstroms, and the composite color, similar to what we would see with our eyes is invisible.

 

c.     Electric burner (800 F)

This is about 700 K, and the plot shows the peak somewhere in the infrared; i.e. at wavelengths greater than 10,000 Angstroms.The composite color is a dark red, pretty similar to what an electric burner looks like.

 

d. Surface of Mars (225 K)

The plot shows the peak somewhere in the infrared; i.e. at wavelengths greater than 10,000 Angstroms.The composite color is invisible; i.e. Mars does not emit much in the visible region of the spectrum.

 

If you calculated these instead of using the webpage, you got full credit.

 

e.††† True or false:If the Sunís surface became much hotter (while the Sunís size remained the same), the Sun would emit more ultraviolet light but less visible light that it currently emits.Explain.

According to the Stefan-Boltzman law, hotter objects will emit more total energy at all wavelengths.If you watch the thermal radiation curve change as you increase the temperature, you will notice that the intensity increases at all wavelengths.So the answer is false, the Sun will emit more light at all wavelengths, not just UV.

 

2.     Mars is known as the Red Planet.Explain in words the origin of its red color.What does your answer to 1(d) above have to do with this?

 

Mars has a significant amount of iron in its surface soil.Iron absorbs at blue wavelengths.So the spectrum we see from Mars is the reflected spectrum of the Sun with some of the blue light removed by the iron in Martian soil.At 225 K, the thermal radiation emitted by the Martian surface peaks in the infrared, and hence does not affect the visible spectrum.

 

3.     Now that you know radio waves are electromagnetic radiation and not sound waves, investigate how a radio works and write a 2-3 paragraph explanation.††† Hereís a list of helpful websites:

http://howthingswork.virginia.edu/radio.html

http://cfcp.uchicago.edu/education/innercity/pdfs-sum02/background.pdf

More technical descriptions for those interested:

http://micro.magnet.fsu.edu/electromag/java/radio/

http://www.arrl.org/tis/info/antheory.html#why

Oscillating electric charges generate electromagnetic waves.A radio transmitter works by using electric current to make electrons in the conductive metal of an antenna oscillate at radio frequencies (i.e. in the radio region of the electromagnetic spectrum).As the radio waves pass a radio antenna, they cause the electrons in the antenna to oscillate at the frequency of the radio wave in response, generating an electric current in the receiving radio antenna like that generated by the transmitting antenna.

††††††††† AM refers to very long wavelength radio waves which are modified in amplitude (strengths) to carry information.Because long wavelengths are scattered less easily, AM radio waves can travel long distances with relatively little interference. FM refers to somewhat shorter wavelength radio waves, which are frequency modulated to carry information.The circuitry in the radio and speakers decodes the signal from the transmitting antenna, converting it to sound waves via vibrations in the speaker system.Since AM and FM waves carry information differently and at different wavelengths, you must select which type you are tuning into.

 

 

4.     Suppose you take a spectrum of light coming from a planet that looks blue to the eye.

a.      Do you expect to see any visible light in the planetís spectrum?

Yes.

††

b.     Is the visible light emitted by the planet, reflected by the planet or both? (Hint: Check out Table 10.2 and Figure 11.9)

Reflected from the Sun.

 

c.     Which (if any) portions of the visible spectrum do you expect to find ďmissingĒ in the planetís spectrum, and why?

Methane absorbs red light, so Iíd expect the spectrum to be missing some of the red wavelengths, making the planet appear blue.


 

5.      

a.      What is the frequency of a visible light photon with wavelength 550 nm (5500 Angstroms)?

5.5x1014 Hz

 

b.     What is the wavelength of a radio photon from an ďAMĒ radio station that broadcasts at 1,120 kilohertz?What is its energy?

268 m

 

c.     What is the energy (in joules) of an ultraviolet photon with wavelength 120 nm?What is its frequency?

1.7x10-18 Joules†††† 2.5x1015 Hz

 

d.     What is the wavelength of an X-ray photon with energy 10 keV (10,000 eV)?What is its frequency?(Hint: recall that 1eV = 1.6x10-19 joules.)

1.2 Angstroms†††††† 2.4x1018 Hz†††††