Particle accelerators, such a s the Large Hadron Collider, use magnetic fields to steer charged particles a round a ring. Consider a proton ring with 36 identical bending mag nets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. What magnetic field strength is needed i n each magnet to steer protons around the ring with a speed of $2.5 \times 10^{7} \mathrm{m} / \mathrm{s}$? Assume that the field is uniform inside the magnet, zero outside.

How does a saturated hydrocarbon differ from an unsaturated hydrocarbon?

Protons having a kinetic energy of

$$5.00 \mathrm{MeV}(1 \mathrm{eV}=1.60 \times \left.10^{-19} \mathrm{J}\right)$$

are moving in the positive x direction and enter a magnetic field $\overrightarrow{\mathbf{B}}=0.0500 \hat{\mathbf{k}} T$ directed out of the plane of the page and extending from x = 0 to x = 1.00 m. (a) Ignoring relativistic effects, find the angle $\alpha$ between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. (b) Calculate the y component of the protons' momenta as they leave the magnetic field.

A mole is approximately the number of protons in a gram of protons. The mass of a neutron is about the same as the mass of a proton, while the mass of an electron is usually negligible in comparison, so if you know the total number of protons and neutrons in a molecule (i.e., its "atomic mass"), you know the approximate mass (in grams) of a mole of these molecules. Referring to the periodic table at the back of this book, find the mass of a mole of each of the following: water, nitrogen $\left(\mathrm{N}_{2}\right),$ lead, quartz $\left(\mathrm{SiO}_{2}\right).$

What is the role of water in the carbon cycle?

Show, by means of drawings, the difference between a saturated and an unsaturated solution.

Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of $2.5 \times 10^7 \mathrm{~m} / \mathrm{s}$ ? Assume that the field is uniform inside the magnet, zero outside.

A reaction that has been considered as a source of energy is the absorption of a proton by a boron-11 nucleus to produce three alpha particles: $_ { 1 } ^ { 1 } \mathrm { H } + _ { 5 } ^ { 11 } \mathrm { B } \rightarrow 3 \left( _ { 2 } ^ { 4 } \mathrm { He } \right)$ This reaction is an attractive possibility because boron is easily obtained from Earth’s crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts to the initiation of uranium fission by slow neutrons. How much energy is released in each reaction?

In a study designed to investigate the effects of a strong magnetic field on the early development of mice, ten cages, each containing three 30-day-old albino female mice, were subjected for a period of 12 days to a magnetic field having an average strength of 80 Oe/cm. Thirty other mice, housed in ten similar cages, were not put in the magnetic field and served as controls. Listed in the table are the weight gains, in grams, for each of the twenty sets of mice.

$$\scriptstyle \begin{array}{c} \hline \text { In Magnetic Field } & \text { Not in Magnetic Field } \\ \hline\end{array}$$

$$\scriptstyle\begin{array}{cccc} \text { Cage } & \text { Weight Gain (g) } & \text { Cage } & \text { Weight Gain (g) } \\ \hline 1 & 22.8 & 11 & 23.5 \\ 2 & 10.2 & 12 & 31.0 \\ 3 & 20.8 & 13 & 19.5 \\ 4 & 27.0 & 14 & 26.2 \\ 5 & 19.2 & 15 & 26.5 \\ 6 & 9.0 & 16 & 25.2 \\ 7 & 14.2 & 17 & 24.5 \\ 8 & 19.8 & 18 & 23.8 \\ 9 & 14.5 & 19 & 27.8 \\ 10 & 14.8 & 20 & 22.0 \\ \hline \end{array}$$

Test whether the variances of the two sets of weight gains are significantly different. Let $\alpha=0.05 .$ For the mice in the magnetic field, $s_{X}=5.67 ;$ for the other mice, $s_{Y}=3.18$.

Two small copper spheres each have radius $1.00 \mathrm{~mm}$. $(a)$ How many atoms does each sphere contain? $(b)$ Assume that each copper atom contains $29$ protons and $29$ electrons. We know that electrons and protons have charges of exactly the same magnitude, but let's explore the effect of small differences. If the charge of a proton is $+e$ and the magnitude of the charge of an electron is $0.100 \%$ smaller, what is the net charge of each sphere and what force would one sphere exert on the other if they were separated by $1.00 \mathrm{~m}$ ?

The triatomic molecular ion $\mathrm{H}_3{ }^{+}$was first detected and characterized by J. J. Thomson using mass spectrometry. Use the bond energy of $\mathrm{H}_2(432 \mathrm{~kJ} / \mathrm{mol})$ and the proton affinity of $\mathrm{H}_2$ $\left(\mathrm{H}_2+\mathrm{H}^{+} \longrightarrow \mathrm{H}_3{ }^{+} ; \Delta H=-337 \mathrm{~kJ} / \mathrm{mol}\right)$ to calculate the heat of reaction for $\mathrm{H}+\mathrm{H}+\mathrm{H}^{+} \longrightarrow \mathrm{H}_3{ }^{+}$.

Indicate whether each of the following statements about magnesium isotopes is true or false.

a. $^{24}_{12}\text{Mg}$ has one more proton than $^{25}_{12}\text{Mg}$

b. $^{24}_{12}\text{Mg}$ and $^{25}_{12}\text{Mg}$ contain the same number of subatomic particles.

c. $^{24}_{12}\text{Mg}$ has one less neutron than $^{25}_{12}\text{Mg}$.

d. $^{24}_{12}\text{Mg}$ and $^{25}_{12}\text{Mg}$ have different mass numbers.

Suppose an experimenter intends to do a regression analysis by taking a total of 2n data points, where the $x_{i}$'s are restricted to the interval [0,5]. If the xy-relationship is assumed to be linear and if the objective is to estimate the slope with the greatest possible precision, what values should be assigned to the $x_{i}$'s?

Calculate the force on an electron in each of the following situations: $3.0 \times 10^{−6}$ m from a proton. Use the following: $q_{e}=-1.6 \times 10^{-19} \mathrm{C}$; $m_{e}=9.1 \times 10^{-31} \mathrm{kg}$; $q_{p}=1.6 \times 10^{-19} \mathrm{C}$; $c=3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$; $k_{C}=9.0 \times 10^{9} \mathrm{N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}$.