Physics PHYS 102
General Astronomy

Problem Set #4

 

After you finish this problem set, you should be familiar with:

Rutherford's atom

absolute zero

energy levels

Bohr's atom

Kirchoff's Laws

blackbodies

Celsius

spectral lines

Stephan-Boltzmann Law

Fahrenheit

elements

Wein's Law

Kelvin

spectrograms

Planck

quantum mechanics

 

Please answer the following questions using sentences and paragraphs.  When it is helpful, please use diagrams and equations. 

  1. Dear Astronomy Student,

It has come to my attention that your name is really Lex Luthor, and that the only reason you are taking Dr. Aikens' astronomy class is to learn the techniques astronomers use to determine the composition of distant astronomical objects. Your hope is that you can learn the composition of the red sun of Krypton, and use this information to destroy Superman forever. Please describe for me exactly what you have learned, and together we can use the information to rid the universe of that meddlesome caped crusader.

Your affectionate partner in crime,

Braniac

 

  1. Dear Braniac,

Before I share with you the secret that will allow me to destroy that super do-gooder, I must know if you are who you claim you are.  Only an ultra-intelligent mechanical android from an alien world would be able to answer these three super-scientific questions: 

    1. How are an atom, a nucleus, an element and an isotope different?
    2. How is the description of an atom given by quantum mechanics different than Rutherford's "miniature solar system" model?
    3. What do scientists mean when they speak of an atomic transition?

If I don't receive a satisfactory answer from you by the due date on Dr. Aikens' next homework assignment, I will know this is merely one of Superman's pitiful attempts at trickery.

Lex Luthor,

Mastermind of Crime

 

  1. The evil Lex Luther, using his knowledge of the spectral lines of the red sun of Krypton, has greatly weakened Superman and is chasing him with the intent of finishing him forever. Superman is trying to escape, but unfortunately there is a red traffic light ahead of him. Since Superman always obeys the law, he must stop for the light, even if doing so means he will be destroyed by Lex. As a bystander, you realize what is about to happen unless you intervene. You quickly decide to help Superman with your vast knowledge of astronomy, and especially the Doppler effect.
    1. Quickly explain to Superman what the Doppler effect is, and briefly mention why it is important to astronomers like yourself.
    2. Explain to Superman how he can change the apparent color of the stop light from red to green by flying toward it. Using the Doppler effect, determine for Superman the velocity he would need to fly toward the stoplight to go through a "green light".

 

  1. Here is a link to an interactive simulation of a blackbody spectrum: link. In this simulation, you can enter the temperature of the black body you are interested it. The simulation will show you a plot of the intensity versus wavelength for a blackbody with that temperature. It will also show you the color that blackbody would appear.  Clicking on the top of the curve will show you the wavelength of the maximum.
    1. What is a blackbody?  If stars are like blackbodies, why are they not black?  How is a star different from a blackbody?
    2. What color would a blackbody at 15,000K appear to the naked eye? At what wavelength does its emission peak?
    3. If a star was white in color, approximately what would its temperature be? What wavelength is "white" light  (Hint: This is a trick question.  Explain why.)
    4. An astronomer discovers a star whose maximum emission is at 40 nm. What is its temperature? What color does it appear to the naked eye?

Now Imagine a star the same size as the Sun, but with half the surface temperature. Assume the surface temperature of the Sun is about 10,000 F.  Without using the simulation above, but just using  the formulas for Wien's Law and the Stephan-Boltzmann law, see if you can answer the following questions: 

    1. At what wavelength would the star emit most of its radiation?
    2. What color would this star appear?
    3. What fraction of the brightness of the Sun is the star, if it is the same distance away?

 

Here are some practice "figure it out rather than memorize" type questions.  They will not be graded as part of the homework (so don't turn them in), but they may be useful as you prepare for the test.  More questions like these can be found in the test practice folder at the library.

1.

A violet photon has a wavelength of 400 nm.  What is its energy?

 

A)

6.88 1019 Joules

 

B)

5.21 1019 Joules

 

C)

4.97 1019 Joules

 

D)

3.62 1019 Joules

 

2.

How many neutrons are there in the nucleus of the isotope 17O of oxygen?

 

A)

9

 

B)

7

 

C)

8

 

D)

17

 

3.

An atom of hydrogen undergoes a collision with another atom in a hot gas in which the energy of collision is about 11 eV.  What is the likely outcome of this collision in terms of the atom? 

 

A)

The electron in the atom will be excited to the second excited level, n = 3, and de-excitation will generate either a La UV Lyman photon or an Ha visible and a La UV photon.

 

B)

The electron in the atom will be excited to the first excited level, n = 2.  Its return to the ground state will produce a La UV Lyman photon.

 

C)

The electron in the atom will be excited to the first excited level, and de-excitation to the ground state will produce a visible photon of Balmer Ha light.

 

D)

The electron of the hydrogen atom will be excited beyond the ionization level (n = infinity); the atom will be ionized and the electron will leave the atom completely.

  

4.

An astronomer measures the spectrum of a star and finds a spectral line at 499 nm wavelength.  In the laboratory, this spectral line occurs at 500 nm.  According to the Doppler effect, this object is

 

A)

moving toward the Earth at 1/500 the speed of light.

 

B)

moving away from the Earth at 1/500 the speed of light.

 

C)

moving toward the Earth at 499/500 the speed of light.

 

D)

moving away from the Earth at 499/500 the speed of light.

  

5.

A star whose surface temperature is 100,000 K will emit a spectrum whose peak wavelength is

 

A)

at ultraviolet wavelengths.

 

B)

at X-ray wavelengths.

 

C)

at visible wavelengths.

 

D)

at infrared wavelengths.

 

6.

A piece of iron is heated from 400 K to 800 K (127C to 527C). The total energy emitted per second by this iron will increase by a factor of

 

A)

296.5.

 

B)

4.

 

C)

2.

 

D)

16.

  

7.

The temperature of boiling water at ordinary pressures on the absolute scale, Kelvin, is

 

A)

273 K.

 

B)

212 K.

 

C)

100 K.

 

D)

373 K.

  

8.

The image formed by an object that is farther away from a convex lens than the focal point is

 

A)

upright,  real

 

B)

inverted, real

 

C)

inverted, virtual

 

D)

none of these