31.3 Substructure of the nucleus  (Page 5/17)

A typical carbon nucleus contains 6 neutrons and 6 protons. The 6 protons are all positively charged and in very close proximity, with separations on the order of 10 ^-15 meters, which should result in an enormous repulsive force. What prevents the nucleus from dismantling itself due to the repulsion of the electric force?

1. The attractive nature of the strong nuclear force overpowers the electric force.
2. The weak nuclear force barely offsets the electric force.
3. Magnetic forces generated by the orbiting electrons create a stable minimum in which the nuclear charged particles reside.
4. The attractive electric force of the surrounding electrons is equal in all directions and cancels out, leaving no net electric force.

The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?

Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.

What are isotopes? Why do different isotopes of the same element have similar chemistries?

Verify that a $2\text{.}3\times {\text{10}}^{\text{17}}\text{kg}$ mass of water at normal density would make a cube 60 km on a side, as claimed in [link] . (This mass at nuclear density would make a cube 1.0 m on a side.)

Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be $2\text{.}3\times {\text{10}}^{\text{17}}{\text{kg/m}}^3$ .

What is the radius of an $\alpha$ particle?

Find the radius of a ${}^{\text{238}}\text{Pu}$ nucleus. ${}^{\text{238}}\text{Pu}$ is a manufactured nuclide that is used as a power source on some space probes.

(a) Calculate the radius of ${}^{\text{58}}\text{Ni}$ , one of the most tightly bound stable nuclei.

(b) What is the ratio of the radius of ${}^{\text{58}}\text{Ni}$ to that of ${}^{\text{258}}\text{Ha}$ , one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than the size of an atom.

The unified atomic mass unit is defined to be $1\text{u}=1\text{.}\text{6605}\times {\text{10}}^{\mathrm{-27}}\text{kg}$ . Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for $c$ and $\mid q_e\mid$ .

What is the ratio of the velocity of a $\beta$ particle to that of an $\alpha$ particle, if they have the same nonrelativistic kinetic energy?

If a 1.50-cm-thick piece of lead can absorb 90.0% of the $\gamma$ rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the $\gamma$ rays?

The detail observable using a probe is limited by its wavelength. Calculate the energy of a $\gamma$ -ray photon that has a wavelength of $1\times {\text{10}}^{-\text{16}}\text{m}$ , small enough to detect details about one-tenth the size of a nucleon. Note that a photon having this energy is difficult to produce and interacts poorly with the nucleus, limiting the practicability of this probe.

(a) Show that if you assume the average nucleus is spherical with a radius $r=r_0{A}^{1/3}$ , and with a mass of $A$ u, then its density is independent of $A$ .

(b) Calculate that density in ${\text{u/fm}}^3$ and ${\text{kg/m}}^3$ , and compare your results with those found in [link] for ${}^{\text{56}}\text{Fe}$ .

What is the ratio of the velocity of a 5.00-MeV $\beta$ ray to that of an $\alpha$ particle with the same kinetic energy? This should confirm that $\beta$ s travel much faster than $\alpha$ s even when relativity is taken into consideration. (See also [link] .)

(a) What is the kinetic energy in MeV of a $\beta$ ray that is traveling at $0.998c$ ? This gives some idea of how energetic a $\beta$ ray must be to travel at nearly the same speed as a $\gamma$ ray. (b) What is the velocity of the $\gamma$ ray relative to the $\beta$ ray?