Consider an electron in its first excited state in a hydrogen atom. Determine its (a) orbital speed, (b) angular speed, (c) linear momentum, and (d) angular momentum.

State where in its domain the given function is continuous, where it is left or right continuous, and where it is just discontinuous.

$$f(x)=\left\{\begin{array}{ll}{x^{2}} & {\text { if } x \leq 1} \\{0.987} & {\text { if } x>1} \end{array}\right.$$

A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate the potential energy.

A line is represented by the equation ax+by=4. (a) When is the line parallel to the x-axis? (b) When is the line parallel to the y-axis? (c) Give values for a and b such that the line has a slope of $\frac{5}{8}$. (d) Give values for a and b such that the line is perpendicular to $y=\frac{2}{5} x+3$. (e) Give values for a and b such that the line coincides with the graph of 5x+6y=8.

Consider a system of three nonidentical particles, each with angular momentum $\frac{3}{2}$. Find the possible values of the total spin $S$ of this system and specify the number of angular momentum eigenstates corresponding to each value of $S$.

The principle quantum number n is associated with (a) the total energy of a state, (b) the orbital angular momentum of the electron's orbit, (c) the z-component of the electron's orbital angular momentum, (d) the electron's spinning angular momentum.

A hydrogen atom is in its first excited state (n = 2). Calculate the potential energy of the system.

A hydrogen atom is in its first excited state (n = 2). Calculate the kinetic energy of the electron.

Find particular solutions. $\frac{d m}{d t}=0.1 m+200$, m(0)=1000

A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate the linear momentum of the electron,

You have available 2,2-dimethylcyclopentanol (A) and 2-bromo-1,1-dimethylcyclopentane (B) and wish to prepare 3,3-dimethylcyclopentene (C). Which would you choose as the more suitable reactant, A or B, and with what would you treat it?

Find each integral three ways: (a) By using substitution. (b) By using even-odd properties of the definite integral. (c) By using trigonometry to simplify the integrand before integrating. (d) Verify the results are equivalent. $\int_{-\pi / 2}^{\pi / 2} \cos (2 x+\pi) d x$

A hydrogen atom is in its first excited state (n = 2). Calculate the linear momentum of the electron.

$\beta^{-}$ decay can occur only in nuclei with what Z values: (a) $Z>82,$ (b) $Z \leq 82,$ or (c) it can occur regardless of the Z value?