# Homework Assignment #3, Astronomy 115

1. Chapter 4, Review Question 2

a.) Infrared Has the longest wavelength, and thus smallest frequency and the lowest energy.

2. Chapter 4, Review Question 9

An element is the smallest chemical unit that can be broken down. Every atom can be classified as one element or another, depending on the number of PROTONs in its nucleus. Five examples of elements are:

• Gold (Au 79 protons)
• Uranium (U 92 protons)
• Potassium (K 19 protons)
• Curium (Cm 96 protons)
• Selenium (Se 34 protons)

3. Chapter 4, Advanced Question 18

If a star has a Balmer Beta line at 486.112 nm what is the star's radial velocity? Is it approaching or receding? (lambdao= 486.133)

Relative to the rest frame, the light from the star has been stretched out by:

Δ λ = 486.133 - 486.112 = 0.021 nm

The doppler formula tells us its speed:

v/c = Δ λ / λo

v/c = 0.021 nm / 486.122 nm

v/c = 4.3e-5= 0.000043

So v = 0.000043 * c

Since the speed of light is 300,000 kilometers/ second, (which equals 3 x 108 meters/ second)
the speed of the star is:

So v = 0.000043 * 300,000 km/s v = 12 km/s

Because the the observed light waves have shorter wavelength than the the rest waves, the light waves have been compressed. So, the star is APPROACHING (not receding).

4. Chapter 4, Advanced Question 20

To make a red stop light turn green you'd have to be moving toward it, (causing a blueshift) fast enough to shrink red light (700 nm) to green (500 nm).
Thus we should regard the red light as the "rest wavelength" in the doppler formula:

v/c = Δ λ / λo

= (700-500)/ 700 = 0.28

So you would need to travel at a speed equal to

v = 0.28 c = 84,000 km/s

By the way, you could also drive away from a green light, and make it look red. You would need to travel at a speed, v, given by: :

v/c = Δ λ / λo

= (700-500)/ 500 = 0.4

v = 0.4 c = 120,000 km/s (2/5 ths of the speed of light!)

In either case you must travel at a sizable fraction of the speed of light. In that case, police have no chance of catching you!

### Chapter 10

5. Chapter 10, review question 2

The corona and the chromosphere can be viewed during a solar eclipse. The photophere is the surface visible when we look at the Sun. Under magnification, it is possible to see the convection cells on the surface of the Sun.

6. Chapter 10, Question 13

Hydrogen fusion means that hydrogen nuclei (protons) can combine to form Helium nuclei. It takes 4 Hydrogens to make one Helium, but the Helium has less mass than the 4 Hydrogens that made it. The mass that is converted into energy. This differs from chemical reactions (like the burning of a log) which only involve the electrons of atoms, not the nuclei.

7. A textbook weighs about 1.5 kilograms (3.3 lbs). A.) How many Joules of energy would be released if the entire book turned into pure energy?

Since the entire book is turned into energy, (unlike fusion in the Sun where only ~ 1% vanishes), M = 1.5 kg E = M c 2

E = 1.5 kg x (3 x 108m/s) 2

E = 1.5 x 9 x 1016 kg x m2/s2

E = 1.3x 1017 Joules

B.) Compare this to the energy used by the entire city of San Francisco in one year: roughly 7.5 x 1016Joules. If you could turn Mass into Energy, could you power The City for a year using one book?

This is enough to power SF for: 1.3x 1017 Joules / 7.5 x 1016Joules/year = 1.8 years

8. Tsar Bomba released 240 x 1015 Joules of energy. Calculate how much mass is lost to produce this energy.

E = 240 x 1015 Joules

E = M c 2

M = E / c 2

M = 240 x 1015 / 9 x 1016 kg

M = 2.6 kilograms ...or about 5 pounds of matter transformed to energy.... producing the largest explosion in human history.

### Chapter 11

9. Chapter 11, Review Question 7

Stellar Parallax is a method for measuring the distances to stars. It works by observing a star from two different perspectives separated by 2 AU along the Earth's orbit. The apperent angular change in the star's position is inversely proportional to its distance. (d = 1/p)

10. The closest star to our solar system is Proxima Centauri at 1.3 parsecs distance.
A.) How long does it take light from Proxima to reach the Earth?
B.) By what angle, (in arc seconds) does Proxima appear to move with respect to the background stars as Earth orbits the Sun.

A.) 1 pc = 3.26 light years. So the distance to Proxima is 1.3 * 3.26 = 4.2 light years. This means it takes light from Proxima 4.2 years to reach us.
B.) Parallax is the amount by which a nearby star appears to move with respect to the background stars due to the Earth's orbital motion. The angle of parallax in arcseconds (P) is given by:

p = 1/d

Where d is the distance in pc. So in the case of Proxima:

p = 1/1.3 = 0.769231 arc seconds.