Electromagnetic Radiation & Telescopes – Review

 

1.     A certain tuning fork has a frequency of 256 Hz.  (a) Given the speed of sound is 343 m/s, what is the wavelength of the sound it makes?  (b) What frequency tuning fork would generate sound waves with wavelength 2.00 m?

2.     Astronomers measure redshift basically as a “fractional change” in wavelength.  For example a redshift of 1 means an increase of 100% over that of the original wavelength.  So, if the original wavelength is 450 nm, a redshift =1 would mean the observed wavelength is 900 nm.  (a) Calculate the original and observed frequencies using these wavelengths.  (b) Classify each wavelength as a certain EMR type and if it is visible give the color.  (c) In order for this change to occur would the source be moving away from or toward the observer?

3.     Be able to state the major types of electromagnetic radiation and the colors of the rainbow in order of increasing frequency.  (a) If placed in this order does the wavelength increase or decrease?  (b) Does the energy per photon increase or decrease?

4.     (a) A certain radio station has a frequency of 99.1 MHz – what is its wavelength?  (b) A radio station with a wavelength of 303 m has what frequency?

5.     Sketch a graph of intensity vs. wavelength and sketch two blackbody curves – one for a hotter object and one for a cooler object.  Make sure to correctly illustrate the effect of temperature on the curve.

6.     (a) A star with temperature 5200 K would emit the greatest number of photons at what particular frequency of radiation?  (b) What is the wavelength of these photons?  (c) The spectrum of this star’s light would be continuous except for a pattern of very narrow and dim dark lines – what causes these lines?  (d) What characteristics of the star can be determined by an analysis of these lines?

7.     A particular hot object emits blackbody radiation.  It emits more energy at a frequency of 3.86 × 10¹³ Hz than at any other frequency.  (a) What type of radiation is it mainly emitting?  (b) Determine the temperature of this object in Kelvin and in Celsius.  (c) What would be an example of an object or substance with these properties?

8.     Two otherwise identical stars rotate at different rates.  How would the spectral lines of the more rapidly rotating star be different from that of the other?

9.     An astronomer observes spectra from two different stars.  The same pattern of lines is apparent in each spectrum.  However the lines from star B are broader than that of star A and the lines from star B are all shifted to longer wavelengths than that of star A.  (a) How are the two stars similar?  (b) What could account for the differences in the spectra of the two stars?

10.  In a particular atom an electron that transitions from orbit 6 to orbit 5 (where orbit 1 = ground state) results in the emission of a photon with wavelength 400 nm (the lower bound of the visible spectrum).  What type of emission would result from a transition from orbit 7 to orbit 5?  Explain.

11.  To build a telescope that can possibly achieve a resolution of 1 milliarcsecond would require what minimum diameter if operating at an ultraviolet wavelength of 350 nm?

12.  A certain telescope has an objective lens with a focal length of 500 mm.  (a) If an eyepiece with focal length 20.0 mm, what will be the magnification?  (b) If a magnification of 120 power is desired, what should be the focal length of the ocular?

13.  The iris of a typical teenager’s eye can range from 1.5 mm to 7.00 mm.  By what factor does the eye’s light gathering capacity increase when the diameter of the iris goes from 1.5 mm to 7.00 mm?

14.  The Hubble Space Telescope has a primary mirror of diameter 2.4 m.  (a) In order to double the light gathering capacity of the HST what size mirror would he needed of the “next generation” space telescope?  (b) By what factor would this conceivably improve its resolution?

15.  The atmosphere affects the use of telescopes at the surface of the Earth.  (a) Consult the chart on page 71 – explain what is meant by the “Radio Window” and the “Optical Window” shown by the Opacity graph at the bottom of Figure 3.9.  (b) Explain how the atmosphere effectively limits optical angular resolution to 1 arcsecond unless special technique or equipment is used.  (c) What are some of the ways that astronomers can solve the problems that the atmosphere presents?

 

Answers:

1.     a. 1.34 m
b. 172 Hz

2.     a. 6.67 × 10¹⁴ Hz; 3.33 × 10¹⁴ Hz
b. visible (purple); infrared
c. away

3.     RMIVUXG; ROYGBIV
a. wavelength decreases
b. energy increases

4.     a. 3.03 m
b. 990 kHz

5.      

6.     a. 5.4 × 10¹⁴ Hz
b. 558 nm
c.
d.

7.     a.
b. 373 K, 100 ºC
c.

8.      

9.     a.
b.

10.   

11.  88 m

12.  a. 25 times
b. 4.2 mm

13.  22 times

14.  a. 3.4 m
b. 1.4 times better

15.  a.
b.
c.