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Phy 3031 Modern physics, Spring 2008
Homework set #8. Due at the start of class on Monday, February 25, 2008.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. (a) If a neutron at rest were to decay into an electron and a proton, what would be the
approximate amount of the kinetic energy of the electron and proton combined?
(b) After the decay, approximately how much Kinetic energy does the electron have?
2. uncharged elementary particle with rest energy mK c2 = 497 MeV. A pion π o is an
uncharged elementary particle with rest energy mπ c2 = 135 MeV. A K o decays into
two π o particles in an average time of 9 × 10−17 s.
(a) After the decay of a K o , at rest in the laboratory, into two π o particles what is
the total energy of one π o , measured in the laboratory?
(b) What is the kinetic energy of this π?
(c) What is the speed of this π o ?
3. Here are some facts:
From the nutrition label on a box of cereal we know that 1 oz of cereal gives 120 Calories
of energy.
Note that 1 calorie is the amount of energy needed to raise 1 gm of water 1◦ C, and
that
1 Cal = 1 kcal = 1000 cal
1 oz = 28.35 g
1 cal = 4.2 J
Assume that the chemical process in the Sun that provides its heat is about as efficient
as that of the human body eating carbohydrates. (This is actually incorrect but was
thought to be true in the early 1900’s. So assume it to be true for this problem.)
The mass of the Sun is 2 × 1030 kg.
The distance from Earth to the Sun is 1.5 × 108 km.
The rate at which energy from the sun lands on earth can be measured by putting a
glass of water outside at noon on a sunny day and is about 300 cal/ m2 s = 1.26 kw/ m2
Here is the problem:
Estimate the lifetime of the sun using these facts.
4. (a) What is the surface temperature of a star whose spectrum has a peak at λ =
500 nm, which is the wavelength of green light.
(b) Does the star appear to be green?