Estimate the lowest possible energy of a neutron contained in a typical nucleus of radius $1.0 \times 10^{-15} \mathrm{m}$ [Hint: a particle can have an energy at least as large as its uncertainty.]

Large telecom companies like AT&T routinely send repair technicians to customers' homes. Although they are skilled laborers, they must usually train on the job, so it takes some time for them to reach a high standard of quality. In addition, their work cannot be constantly supervised. Explain why an efficiency wage could help telecom companies to increase the productivity of repair techs.

An alpha particle (the nucleus of a helium atom) has a mass of $6.64 \times 10^{-27}$ kg and a charge of +2e. What is the direction of the electric field that will balance the gravitational force on the particle?

15. The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit $1.06 \times 10^{-10}\ \mathrm{m}$ in diameter. (a) If the average speed of the electron in this orbit is known to be $2.20 \times 10^{6}\ \mathrm{m} / \mathrm{s},$ calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?

In the following exercise, we study the connection between sets and combinations.

Given a set with n elements,

(a) what is the number of subsets of size 0? of size 1? of size 2? of size n?

(b) Using your answer from part (a) give an expression for the total number of subsets of a set with n elements.

A photon with a wavelength of $1.00 \times 10^{-13} \mathrm{~m}$ is ejected from an atom. Calculate its energy and explain why it is a $\gamma$ ray from the nucleus or a photon from the atom.

Differentiate the function.

f(t) = t$^2$sec t

Leslie Matrices For each of the following Leslie matrices, a. find a population of size 10,000 for which the proportion of the population in each age group stays the same from one year to the next, and b. tell by what factor the population grows or declines each year.

$$\left[\begin{array}{ll}0.2 & 0.3 \\ 0.4 & 0.1\end{array}\right]$$

A load $P$ will be supported by a structure consisting of a rigid bar $A B C D$, a polymer $\left[E=2,300 \mathrm{ksi} ; \alpha=2.9 \times 10^{-6} /{ }^{\circ} \mathrm{F}\right]$ bar (1), and an aluminum alloy $[E=10,000 \mathrm{ksi} ; \alpha=12.5 \times$ $10^{-6} / \mathrm{F}$ ] bar (2) as shown in Figure P5.61. Each bar has a crosssectional area of $2.00 \mathrm{in}^2$. The bars are unstressed when the structure is assembled at $30^{\circ} \mathrm{F}$. After a concentrated load of

All seeds need light to germinate.

When a method's return type is a class, what is actually returned to the calling program?

• 1. An object of that class
• 2. An alias to an object of that class
• 3. Only the values in the object that the method accessed
• 4. A reference to an object of that class
• 5. Nothing, the return type is strictly for documentation in this situation

Which produces more energy-the fission of a single uranium nucleus or the fusing of a pair of deuterium nuclei? The fission of a gram of uranium or the fusing of a gram of deuterium? (Why do your answers differ?)

Simplify.

$$t(5 t-9)-2 t$$

Which "feels" a greater pull due to gravity, a heavy object or a light object? So why do heavy objects not accelerate faster than light objects?