Physics 110: Homework #1 Solutions

1.1

m. Since this radiation lies in the X-ray band, it does not reach the Earth's surface. m for Hz, which is in the visible band (and has a color between orange and yellow) and, therefore, does reach the Earth's surface.

1.2

Flux quantifies the amount of energy per unit area carried by electromagnetic waves. At the orbit of Venus the flux would be higher than the flux at Earth by an amount , which is about a factor of 2.

1.3

The only properties that matter are the temperature and the emitting surface area of the blackbody. Wien's law says that the peak wavelength of a blackbody spectrum is inversely proportional to its temperature. A star with a temperature 10 times that of the Sun (60,000 K) would have a peak wavelength at . Even though this is in the ultraviolet band, radiation from a hotter blackbody is brighter at all wavelengths, so the star would emit substantial radiation in the visible band and hence, all other things being equal, you would be able to see it.

1.4

In order for red light to appear green due to relative motion (the Doppler effect) the observer would need to be approaching the traffic light at a substantial speed. The change in wavelength from red to green light is m or, alternatively, a fractional change in wavelength of . (The minus sign shows that the observer and traffic light are approaching.) This means that your speed would need to be roughly 20% of the speed of light or 37,000 miles per second. You were thrown in jail for speeding and reckless driving, too.

1.5

A hot dense gas emits a continuous spectrum over a very large range of wavelengths, while a thin gas produces a line spectrum with emission only at a set of discrete wavelengths. The only property of an ideal dense gas (i.e., blackbody) that you can learn about is the temperature (and its size if you know its distance). From a thin gas one can learn about temperature, composition, and motions, which provide greater insight into its nature.

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