Phsx 2220 - Homework #13
41-1. How many electron states are there in the following shells:
(a) n = 4; (b) n = 1; (c) n = 3; (d) n = 2?
41-2. What are the four quantum numbers for the two electrons of the
helium atom in its ground state?
43-3. Calculate the distance of closest approach for a head-on collision
between a 5.30 MeV alpha particle and the nucleus of a copper atom.
43-4. Because a nucleon is confined to a nucleus, we can take the
uncertainty in its position to be approximately the nuclear radius
R. What does the uncertainty principle say about the kinetic
energy of a nucleon in a nucleus with, say, A = 100? (Hint: take
the uncertainty in momentum ∆p to be the actual momentum p.)
43-5. Consider an initially pure 3.4 g sample of 67Ga, an isotope that has
a half-life of 78 h. (a) What is its initial decay rate?
(b) What is its decay rate 48 h later?
43-6. A radioactive isotope of mercury, 197Hg, decays into gold, 197Au,
with a disintegration constant of 0.0108 h-1. (a) Calculate its
half-life. What fraction of a sample will remain (b) after three
half-lives and (c) after 10.0 days?
43-7. A 238U nucleus emits a 4.196 MeV alpha particle. Calculate the
disintegration energy Q for this process.
44-8. (a) How many atoms are contained in 1.0 kg of pure 235U? (b) How
much energy, in joules, is released by the complete fissioning of
1.0 kg of 235U? Assume Q = 200 MeV. (c) For how long would this
energy light a 100 W lamp?
44-9. Calculate the energy released in the fission reaction
235U + n –> 141Cs + 93Rb + 2n.
Needed atomic and particle masses are
235U 235.04392 u 93Rb 92.92157 u
141Cs 140.91963 u n 1.00867 u.
44-10. Verify that the fusion of 1.0 kg of deuterium by the reaction
2H + 2H –> 3He + n (Q = +3.27 MeV)
could keep a 100 W lamp burning for 3 x 104 y.
