AST1110-lab5
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AST 1110: Planetary Astronomy
Spring 2024
Lab 5 (30 points) Name: Jenna McCarthy
Spectroscopy and Radiation Laws
Learning Goals
Explain the inverse square law for light
Describe how spectroscopy can be used to characterize a light source
Describe how the Doppler effect changes the light received from a light source. This lab is based on information from Chapter 5
. You can refer to the chapter during lab but remember to write your answers in your own words. Figure 1-An illustration of the inverse square law of light
1.
The intensity of a light source obeys an inverse square law. Explain what this means. The inverse square law is an important principle in physics, that dictates the intensity of a physical quantity or effect, such as light or sound, diminishes proportionally to the square of the distance from its source.
Figure 2-Inverse Square Law showing relative intensity versus distance from the light source
Let’s say that in Figure 2 the intensity, I has a value of 100 Watts at distance r. I = 100 Watts in Figure 2 Use I = 100 for all the examples below.
2.
What is the relative intensity in Watts at a distance 2r from the point source? Use the number given in Figure 2 for a distance 2r. 100/4 = 25 W/m²
3.
What is the relative intensity in Watts at a distance 4r from the point source? Use
the number in figure 2.
100/16 = 6.25 W/m²
4.
What is the relative intensity in Watts at a distance 8r from the point source? 100/64 = 1.56 W/m²
5.
Will you always measure an intensity of 100 Watts from a 100 Watt light bulb? Explain your answer. No, you won't consistently measure an intensity of 100 Watts from a 100 Watt light bulb because the 100-watt rating pertains to the power consumption of the bulb, not the luminous intensity it emits.
With distances in AU, Sunlight at Earth’s location (1 AU) has a brightness of 1 sol. Brightness
=
1
distance
2
2
6.
In comparison, how bright is sunlight at Mercury’s distance of 0.387 AU from the Sun? Show your work using the brightness equation given above.
6.68
=
1
(
0.387
)
2
The brightness of the sunlight at Mercury’s distance from the Sun is about 6.68 times the intensity at 1 AU.
7.
How bright is sunlight at Venus’ distance of 0.723 AU from the Sun? Show your work.
1.91
=
1
(
0.723
)
2
The brightness of the sunlight at Venus’ distance from the Sun is about 1.91 times the intensity at 1 AU. 8.
How bright is sunlight at Neptune’s distance of 30 AU from the Sun? Show your work. 0.00111
=
1
(
30
)
2
The brightness of the sunlight at Neptune’s distance from the Sun is about 0.00111 times the intensity.
3
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Figure 3-temperature (K) vs distance from Sun (AU)
9.
Look at Figure 3. In general, what is the relationship between a planet’s predicted
temperature and the planet’s distance from the Sun?
The further away from the sun, the lower the temperature. 10.Based on Figure 3 explain which planets have the biggest difference between their Range of measured temperatures and their Predicted temperature. Mercury, Mars, and Pluto have the biggest differences between their range of measured temperatures and their predicted temperatures. 11.Describe some other energy sources that could contribute to a planet’s temperature, other than just sunlight. Carbon dioxide, water vapor, methane, and/or nitrous oxide.
4
Figure 4-The image above shows Earth’s orbital motion around the Sun. It is not to scale and is shown at a slight angle
Figure 4 shows Earth’s orbital motion around the Sun. This combines concepts from Chapters 3, 4 and 5.
12.Based on Figure 4, when should the Sun be at its brightest
as seen from Earth? Explain your answer.
January 3
rd
because Earth is the closest to the sun. 13.When should the Sun be at its faintest
, as seen from Earth? Explain your answer.
July 4
th
because the Earth is going to be the farthest away from the sun.
14.Why is Colorado Springs not at its hottest on January 3 every year? Because we are in the winter solstice still. 5
Figure 5-A light source in motion will exhibit a Doppler shift Another important Chapter 5 concept that we’ll review today is the Doppler Effect
. 15.Explain why the observer on the left in the image above sees something different
from the observer on the right even though they are both looking at the same object. 16.Based on the Doppler effect, what is the difference between a light source that shows a redshift and a light source that shows a blueshift? For the next part of the lab, use this Spectrum Constructor animation
. Note that you can
always refresh the page to reset back to the original settings. 17.Describe the steps you can take to use this animation to demonstrate Wien’s Law. (Hint: in the top left under Continuous Spectrum, click the box for Thermal.)
18.Describe the steps you can take to use this animation to show the Doppler effect.
(Hint: Use Absorption spectra. The % of c box means % of the speed of light)
6
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Figure 6-An example spectrum
19.Is Figure 6 showing an absorption spectrum or emission spectrum?
20.Describe what the spectrum in Figure 6 looks like in the Diffraction grating view on the animation linked above.
Figure 7- An example spectrum
21.Is Figure 7 an absorption spectrum or emission spectrum?
22.Describe what the spectrum in Figure 7 looks like in the Diffraction grating view on the animation.
7
Figure 8-Three different spectra of Sodium, illustrating the Doppler effect
23.Which of the examples of Sodium in Figure 8 is Sodium at rest, and which is showing Sodium with the largest Doppler effect? Is the Doppler effect shown a redshift or a blueshift? 24.Use the Absorption spectra in the animation to look at each of these elements on
their own. List the wavelengths of the first 5 spectral lines for each element in the
animation, going from shortest wavelength toward longest. Spectrum
1
st
line (nm)
2
nd
line (nm)
3
rd
line (nm)
4
th
line (nm)
5
th
line (nm)
Mercury
n/a
Lithium
Hydrogen
n/a
Neon
Helium
8
25.Use the 4
th
line of Hydrogen listed above in your table as “data” in the equation below. The known value of this spectral line (the hydrogen-alpha line) is 656.28 nm. Determine the percent error between your data and the known value.
%
error
=
|
(
(
data
−
known
)
known
)
|
×
100
Recall the discussion of electron energy levels from Chapter 5. Figure 9 is an example of electron energy levels for hydrogen for electrons dropping from excited states back to
energy level 2. This is known as the Balmer series of hydrogen and produces wavelengths of visible light. Figure 9-The electron transitions for hydrogen that produce wavelengths of visible light
26.What happens to the energy of the electron in an atom when the atom emits a photon? Does the electron stay at the same energy, or does it increase or decrease in its energy level?
27.What type of spectral line is produced when an atom’s electron loses energy? 9
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28.What type of spectral line is produced when an atom’s electron gains energy? 29.Describe how the properties of radio waves (including energy, speed, wavelength, and frequency) are di
erent from the properties of visible light.
ff
30.Describe how the properties of x-rays (including energy, speed, wavelength, and frequency) are di
erent from the properties of visible light?
ff
10