35. Special Relativity

FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at (a) x=0.000 mm,

A Geiger counter is used to measure the decay of a radioactive isotope produced in a nuclear reactor. Initially, when the sample is first removed from the reactor, the Geiger counter registers 15,000 decays/s. 15 h later the count is down to 5500 decays/s.b. At what time after the sample's removal from the reactor is the count 1200 decays/s?

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36.b. Write the equation that expresses the conservation of relativistic energy for this decay. Your equation will be in terms of the three masses mₙ, mₚ and mₑ and the relativistic factors yₚ and yₑ.

The starship Enterprise, of television and movie fame, is powered by combining matter and antimatter. If the entire 400-kg antimatter fuel supply of the Enterprise combines with matter, how much energy is released? How does this compare to the U.S. yearly energy use, which is roughly 1.0 * 10^20 J?

FIGURE EX39.14 is a graph of |ψ(x)|^2 for an electron.c. What is the probability that the electron is located between x=1.0 nm and x=2.0 nm?

Consider the electron wave function ψ(x)={√c 1−x^2 |x|≤1 cm 0 |x|≥1 cmwhere x is in cm.d. If 10^4 electrons are detected, how many will be in the interval 0.00 cm≤x≤0.50 cm?