31.3 Substructure of the Nucleus

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 fo…

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

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

(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.

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?

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.

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 the exercise.)