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Solutions for class #6 from Yosumism website
Problem 48:
Lab Methods }Uncertainty The general equation for uncertainty is given by , where and is the generalized standard deviation of quantity. So, for this case, one has and thus its uncertainty is given by. (Basically, one has and .) This is choice (C).
YOUR NOTES:
Problem 49:
Advanced Topics }Scintillator The maximal speed the muons can travel at is slightly less than c. Thus, since the distance is , the time required would be. The largest scintillator time is the one closest to this, which is 1 ns, as in choice (B).
Atomic }Orbitals Eliminate (E) immediately since the superscripts do not add to 11. Each superscript stands for an electron. Eliminate (B) because the s orbital can only carry 2 electrons. Ground state means none of the electrons are promoted, and there are no states with unfilled gaps in them. Eliminate (A) since it promotes the 2p electron to 3s, leaving a unfilled orbital of lower energy. Eliminate (D) since it promotes the 3s electron to 3p, leaving an empty orbital of lower energy. Choice (C) is it.
Optics }Speed of Light The speed of light is related to the index of refraction by. Thus, the minimal velocity the particle must have is , since.
YOUR NOTES:
Problem 70:
Special Relativity }Gamma , where ETS supplies the total energy to be 100 times the rest energy. Thus, , but since , where , one has , as in choice (D).
Statistical Mechanics }Distributions The Fermi-Dirac distribution, in general, gives the number of states in to be , where is the total number of states. (The Fermi-Dirac distribution is used since there are only two states.) Define and. The number of states in 1 is just , which is choice (B).
YOUR NOTES:
Problem 72:
Statistical Mechanics }Heat Capacity The heat capacity is just , where ETS generously supplies U, the internal energy. Since and are constants, the first term is trivial.
Statistical Mechanics }Entropy The third law of thermodynamics says that. Also, the statistical definition of entropy is just , where Z is the partition function. For this problem, one has. For high temperatures, one has , since for small x (and then for very small x). Thus the entropy behaves as in choice (C).
YOUR NOTES:
Problem 75:
Advanced Topics }Binding Energy The binding energy for heavy atoms ( ) is about. The change in binding energy is the kinetic energy, thus the Helium atom has a kinetic energy of
. (The binding energy of He is ignored.) This is much larger than the kinetic energy of the He nucleus.
