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College Physics 2017

Educators

Problem 1

Determine the number of (a) electrons, (b) protons, and (c) neutrons in iron $\left(\frac{56}{26} \mathrm{Fe}\right)$

Lisa T.

Problem 2

The atomic mass of an oxygen atom is 15.999 u. Convert this mass to units of (a) kilograms and (b) $\mathrm{MeV} / \mathrm{c}^{2}$

Lisa T.

Problem 3

Find the nuclear radii of the following nuclides: (a) $_{1}^{2} \mathrm{H}$ (b) $^{60}_{27} \mathrm{Co}$ (c) $^{197}_{79} \mathrm{Au}$ (d) $_{94}^{239} \mathrm{Pu}$

Lisa T.

Problem 4

Find the radius of a nucleus of (a) $_{2}^{4}$He and (b) $^{238}_{93}$U

Lisa T.

Problem 5

Using $2.3 \times 10^{17} \mathrm{kg} / \mathrm{m}^{3}$ as the density of nuclear matter, find
the radius of a sphere of such matter that would have a mass equal to that of Earth. Earth has a mass equal to $5.98 \times 10^{24} \mathrm{kg}$ and average radius of $6.37 \times 10^{6} \mathrm{m}$

Lisa T.

Problem 6

Consider the $^{65}_{29} \mathrm{Cm}$ nucleus. Find approximate values for its (a) radius, (b) volume, and (c) density.

Lisa T.

Problem 7

An alpha particle $\left(Z=2, \text { mass }=6.64 \times 10^{-27} \mathrm{kg}\right)$ approaches to within $1.00 \times 10^{-14} \mathrm{m}$ of a carbon nucleus (Z = 6). What are (a) the maximum Coulomb force on the alpha particle, (b) the acceleration of the alpha particle at this time, and (c) the potential energy of the alpha particle at the same time?

Lisa T.

Problem 8

Singly ionized carbon atoms are accelerated through $1.00 \times 10^{3} \mathrm{V}$ and passed into a mass spectrometer to determine the isotopes present. (See Topic 19.) The magnetic field strength in the spectrometer is 0.200 T. (a) Determine the orbital radii for the $^{12} \mathrm{C}$ and the $^{13} \mathrm{C}$ isotopes as they pass through the field. (b) Show that the ratio of the radii may be written in the form
$$\frac{r_{1}}{r_{2}}=\sqrt{\frac{m_{1}}{m_{2}}}$$

Lisa T.

Problem 9

(a) Find the speed an alpha particle requires to come within $3.2 \times 10^{-14} \mathrm{m}$ of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

Lisa T.

Problem 10

At the end of its life, a star with a mass of two times the Sunâ€™s mass is expected to collapse, combining its protons and electrons to form a neutron star. Such a star could be thought of as a gigantic atomic nucleus. If a star of mass $2 \times 1.99 \times$ $10^{30} \mathrm{kg}$ collapsed into neutrons $\left(m_{n}=1.67 \times 10^{-27} \mathrm{kg}\right)$ what would its radius be? Assume $r=r_{0} A^{1 / 3}$.

Lisa T.

Problem 11

Find the average binding energy per nucleon of (a) $_{12}^{24} \mathrm{Mg}$ and (b) $^{85}_{37} \mathrm{Rb}$

Lisa T.

Problem 12

Calculate the binding energy per nucleon for (a) $^{2} \mathrm{H}$, (b) $^{4} \mathrm{He}$ (C) $^{56} \mathrm{Fe}$, (d) $^{238} \mathrm{U}$.

Lisa T.

Problem 13

A pair of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ are called mirror isobars. (The atomic and neutron numbers are interchangeable.) Binding - energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charge independence means that the protonâ€“proton, protonâ€“neutron, and neutronâ€“neutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei $^{15}_{8} \mathrm{O}$ and $_{7}^{15} \mathrm{N}$.

Lisa T.

Problem 14

The peak of the stability curve occurs at $^{56} \mathrm{Fe},$ which is why iron is prominent in the spectrum of the Sun and stars. Show that $^{56} \mathrm{Fe},$ has a higher binding energy per nucleon has a higher binding energy per nucleon than its neighbors $^{55} \mathrm{Mn}$ and $^{59} \mathrm{Co}$. Compare your results with Figure 29.4.

Lisa T.

Problem 15

Two nuclei having the same mass number are known as isobars. (a) Calculate the difference in binding energy per nucleon for the isobars $^{23}_{11} \mathrm{Na},$ and $^{23}_{12} \mathrm{Mg},$ (b) How do you account for this difference? (The mass of $^{23}_{12} \mathrm{Mg}=22.994127 \mathrm{u} . )$

Lisa T.

Problem 16

Calculate the binding energy of the last neutron in the $^{43}_{20} \mathrm{Ca}$ nucleus. Hint: You should compare the mass of $^{43}_{20} \mathrm{Ca}$ with the mass of $^{43}_{20} \mathrm{Ca}$ plus the mass of a neutron. The mass of $_{20}^{12} \mathrm{Ca}=$ 41.958 622 u, whereas the mass of $\underset{20}{43} \mathrm{Ca}=42.958770 \mathrm{u}$

Lisa T.

Problem 17

Radon gas has a half - life of 3.83 days. If 3.00 g of radon gas is present at time t 5 0, what mass of radon will remain after 1.50 days have passed?

Lisa T.