ASTRONOMY 1000.1 A Sky & Planets
Saint Mary’s University, Astronomy and Physics, Prof. I. Short
Solutions 3
Due: Wednesday, 24 November 2010
Total: 30 marks
Note: Be sure to show your work in all answers – your grade will be based partly on your
reasoning!
1. Radio waves, and infrared (IR) radiation from TV remotes, are harmless to skin
tissue, but ultraviolet (UV) and X-ray band radiation is quite harmful. Explain
this difference in terms of the basic nature of electromagnetic (EM) radiation.
Which mathematical law of physics pertaining to radiation helps explain this
situation? (I’m not looking for a biological explanation!)
ANSWER: (4 marks) Photon energy increases with decreasing wavelength OR
increasing frequency, (OR “Planck’s Law” OR “E=hν” OR “hc/λ”)
AND X- and UV rays have shorter wavelengths (higher frequencies) than
IR and radio waves, SO the photons have higher energy.
2. (4 marks) Infrared (IR) cameras can detect humans at night even when it’s
completely dark.
a) Why? Ie. What is the origin and cause of the IR radiation being detected
by the IR cameras?
ANSWER: (2 marks) Blackbody radiation, and/or radiation due to the
excess internal heat of humans
b) Why are we able to see people in the visible band with our eyes during the
day? Ie. what is the source of that radiation? How is the source different
from that of the IR radiation of part a)?
ANSWER: (2 marks) Reflection and/or light (or photons) from an external
source (Sun, lamp, etc.) bouncing off of us
3. (4 marks) Say there is a dense, opaque (ie not transparent!) cloud of interstellar
gas in space that is very cold (ie. has a surface temperature, TSurf, of only 100 K
(“Kelvins”).
a) What is TSurf for this cloud on the Celsius (or “centigrade”, oC)
temperature scale? Show your work!
ANSWER: (2 marks) T = 100K – 273 = -173 C
b) (2 marks) Suppose you wanted to detect the blackbody radiation coming
from this cloud. In which band of the electromagnetic (EM) spectrum
would you have to make your observation? Explain!
ANSWER: (2 marks) IR band. Explain: Peak wavelength is inversely
related to surface temperature (OR Wien’s Law OR “λpeak=W/TSurf”)
4. (6 marks altogether) Say you measure the flux of light (maybe with the light
meter in your digital camera) from an object glowing brightly with blackbody
radiation (like a very hot piece of metal) that is 20 m away, and measure it to be 1
W/m2 (Watt/meter2). Hint: You don’t really need to look up any constants like
“σ” or “π” – we just want the ratio of one flux measurement to the previous one!
a) Now you approach the object so that you are only 10 m from it and
measure the flux from it again. How does this value compare to your last
value? Show your work!
ANSWER: (3 marks) Inverse square law: ½ distance  (2)^2 = 4 × flux. If
you did some legitimate math with the f=L/4πd2 formula to get 4, full marks.
b) Suddenly, the object’s surface temperature, TSurf, drops to ½ of what it was
before. How does the measured flux now compare to your last value at
your position of 10 m away? Show your work!
ANSWER: (3 marks) Surface flux (F) goes as TSurf4  half the TSurf 
(1/2)^4 = 1/16 the flux. If you did some legitimate math with the F=σT4
formula (Stefan-Boltzmann law) to get 1/16, full marks.
5. ( 8 marks) Approximate sketches are okay, BUT the axes must be labeled!!
a) Suppose you were to look though a prism at the light emitted by the solid
tungsten filament of a household (incandescent) light bulb. Assume the filament
has a surface temperature, TSurf, of 7000 K when the bulb is turned “on”.
Describe what the spectrum would look like and draw a graph of brightness (say,
flux (f) or luminosity (L)) versus wavelength (λ) for the spectrum (note that the
fact that the filament is tungsten does not matter!). Be sure to label the axes of
your plot and any features of interest in your spectrum. Which one of Kirchoff’s
laws of radiation describes this situation?
ANSWER: (2 marks) Blackbody (or continuous) spectrum. Kirchoff’s first
law.
Sketch (2 marks) - see next page
b) Now suppose you were to look though the prism at the light emitted by the
thin hot gas in a fluorescent light tube filled with hydrogen. Describe what the
spectrum would look like and draw a graph of brightness versus wavelength (λ)
for the spectrum. (Hint: there is a Figure in Chapter 4 of the text that will help!).
Be sure to label the axes of your plot and any features of interest in your
spectrum. (Do not worry about the exact details of the wavelengths of the
spectral lines!) Which one of Kirchoff’s laws of radiation describes this situation?
ANSWER: ( 2marks) Emission line (OR bright line) spectrum. Kirchoff’s
second law
Sketch (2 marks) Don’t worry about the placement or number of the
emissions lines – full marks if you drew any kind of emission line spectrum, with
axes labeled.
6. (4 marks) The “Big Bang Theory” in cosmology is based in part on the
idea that the Universe is expanding, which means that all distant galaxies are
receding rapidly from us and from each other. This idea is based on the
observation that the light we receive from every distant galaxy, seen in any
direction, has a spectrum in which the spectral lines are greatly red-shifted.
(This question can be answered based on the chapter on radiation - you do not
need to study the chapter on cosmology near the end of the book!)
a) Explain what red-shift means, and how this observation supports the idea
that galaxies are receding. (Be sure to state which radiation effect is
involved.)
ANSWER: (2 marks) Red-shift: A Doppler shift (or Doppler effect) that
increases the wavelength (and/or decreases the frequency) of radiation (or,
decreases the photon energy!). This shift is due to a source of radiation
receding from the observer.
b) Suppose that all distant galaxies were approaching us instead. How
would the spectrum of their emitted light be affected in that case?
Explain!
ANSWER: (2 marks) The galaxies would all have Doppler shifts toward
shorter wavelengths (or higher frequencies) and/or be blue-shifted.