Activity: Determining Red-Shift in a Receding Star

Instructional Objectives
Time Needed for Activity
Target Grade Level
Materials
Background Information & Questions
Web Resources

Instructional Objectives:

Students will -

1. manipulate multivariable algebraic formulas,
2. understand velocity, wavelength and frequency,
3. study the Doppler effect,
4. determine the amount of red-shift in light from a receding star.

Time Needed For Activity:

45 minutes

Target Grade Level:

Advanced high school students.

Materials:

• Calculator
• Dictionary

Background Information and Questions:

Part 1: LIGHT WAVES

Light is best described as a wave. All waves are characterized by a wavelength and a frequency.

The wavelength describes the distance between the crest of each cycle. The frequency is the number of crests that pass any given point every second. Visible light waves range in wavelength from approximately 400 nanometers
(400 nm = 400 x 10^-9m) for violet colors to about 700 nanometers for red. Correspondingly, violet has a frequency of about 7.5 x 10¹⁴ Hz (where 1 Hz is equal to 1 cycle/second) and red has a frequency of 4.3 x 10¹⁴ Hz.

Light is a type of electromagnetic radiation. Other types of electromagnetic radiation like ultraviolet light, infrared light, radio waves and X-rays also travel in the form of a wave but at wavelengths to which our eyes are insensitive.

Sound is not electromagnetic radiation, but sound is a wave as well. Higher pitches are caused by higher frequencies of vibrating molecules that reach your eardrum. Lower pitches are likewise caused by lower frequencies.

Questions:

1. What color has the longest wavelengths?
2. What color has the shortest wavelengths?
3. What color has more crests of its wave passing a given point in one second? Explain.
4. Look up the prefixes "ultra" and "infra" in the dictionary. Explain why the wavelengths just out of the visible spectrum are referred to as ultraviolet and infrared.

Part 2: DOPPLER EFFECT

If a wave source is moving, the crests of its waves get bunched together in front of the wave source. If the wave crests are bunched together, their frequency increases. In the case of a sound wave, the pitch is higher. Behind the wave source, the waves spread out and the pitch is lower.

In the case of light we use the terms "blue-shift" and "red-shift" to describe how the DOPPLER EFFECT changes the wavelength of the light. Being blue-shifted or red-shifted doesn't mean that the light necessarily becomes blue or red. It means simply that the light's wavelength either is shortened (blue shifted) because the object giving off the light is approaching, or is lengthened (red-shifted) because the object is moving away from the observer.

Part 3: DETERMINING THE COMPOSITION OF STARS

When energized atoms and molecules vibrate, they give off massless light particles called photons. These photons travel as a wave, but because of quantum energy effects, a particular type of atom or molecule gives off only certain wavelengths of photon light. For example, when hydrogen atoms are giving off energy in the form of light, they emit light specifically at wavelengths of 410.2 nm, 434.0 nm, 486.1 nm, and 656.3 nm. This is called the emission spectra of hydrogen.

Scientists can use the emission spectra of atoms and molecules to study the composition of stars. Scientists need simply to look very carefully at the intensity and wavelengths of the light given off by the star. A star containing hydrogen, for example, would have intense peaks of energy at 410.17 nm, 434.05 nm, 486.13 nm, and 656.28 nm. These hydrogen emission peaks would be in addition to the ones associated with the other elements contained in the star.

Part 4: RECEDING STARS

In the 1920's, Edwin Hubble, while studying the stars of distant galaxies, found that for some, their emission spectra had peaks at 411.54 nm, 435.50 nm, 487.75 nm, and 658.47 nm. Hubble knew that these wavelengths did not correspond to any known element and that it was not likely that a combination of other elements or molecules was responsible. He did notice that these spectral lines corresponded to hydrogen's emission spectra except that they were all 0.0033 percent longer in wavelength than they should have been for a hydrogen spectra. Hubble deduced that this red-shift must be because of a Doppler effect. His calculations showed that these galaxies must be moving away from earth at 1 x 10⁶ m/s (one million meters per second)!

Part 5: VERIFY HUBBLE'S WORK THAT SHOWS THE UNIVERSE IS EXPANDING

For all waves, the product of wavelength and frequency gives the velocity of the wave where (lambda) is the wavelength and f is the frequency.

v = (lambda) f

In the case of light and other electromagnetic radiation, however, the velocity is always fixed at 3 x 10⁸ m/s. This speed of light is assigned the variable c.

vlight = c = 3 x 10⁸ m/s, or more precisely, c = 2.99792458 x 10⁸ m/s

Use c = 2.9979 x 10⁸ m/s for any calculations below. Also, use the appropriate number of significant digits.

Questions:

1. What would the frequency be of a violet light wave with wavelength of 410.17 nm?
2. What frequency is associated with 434.05 nm?
3. What frequency is associated with 486.13 nm?
4. What frequency is associated with 656.28 nm?
5. Imagine the hydrogen atoms in one of Hubble's distant stars emitting a photon of light at a wavelength of 410.17 nm. If that particular photon were headed directly TOWARD Earth, how much CLOSER to us would that photon be after one second? (Recall that the distance, d, that an object travels in a time, t is given by d = vt where v is the object's velocity.)
6. Now if the star that emitted the photon were traveling AWAY from Earth at 1 x 10⁶ m/s, how much FARTHER from Earth would the star be after one second?
7. After one second, what is the distance between our initial photon and its star?
8. Our initial photon would be followed by many, many more just like it, each behaving similarly to the first. After one second, how many wave cycles of photons would stretch between the distant star and our initial photon?
9. What is the average wavelength of this photon light? (Hint: Use your answers from 4 and 5 above.) Compare this with what Hubble saw.
10. Convince yourself of the validity of this process by repeating questions 2 through 6 for one more of the hydrogen emission spectra peaks at wavelengths 434.05 nm, 486.13 nm, or 656.28 nm. (Choose (a) the distance the photon travels toward Earth, (b) the distance the star moves away from Earth, (c) the distance between the photon and the star, (d) the number of cycles between the star and the photon, (e) the effective red-shifted wavelength.)
11. If you were driving in a VERY fast car, how would the things you approach look different from normal? How would the things you drive away from look different? Explain.
12. Why do you think Hubble's discovery that the universe is expanding would have been impossible without instruments that could precisely measure emission spectra?

Web Resources:

Hubble Telescope Pictures
http://www.stsci.edu/pubinfo/Pictures.html