31.7 Tunneling

A 2.00-T magnetic field is applied perpendicular to the path of charged particles in a bubble chamber. What is the radius of curvature of the path of a 10 MeV proton in this field? Neglect any slowing along its path.

(a) Write the decay equation for the $\alpha$ decay of $^{235} \text{U}$. (b) What energy is released in this decay? The mass of the daughter nuclide is 231.036298 u. (c) Assuming the residual nucleus is formed in its ground state, how much energy goes to the $\alpha$ particle?

A physicist scatters $\gamma$ rays from a substance and sees evidence of a nucleus $7.5 \times 10^{–13} \text{m}$ in radius. (a) Find the atomic mass of such a nucleus. (b) What is unreasonable about this result? (c) What is unreasonable about the assumption?

A frazzled theoretical physicist reckons that all conservation laws are obeyed in the decay of a proton into a neutron, positron, and neutrino (as in $\beta^{+}$ decay of a nucleus) and sends a paper to a journal to announce the reaction as a possible end of the universe due to the spontaneous decay of protons. (a) What energy is released in this decay? (b) What is unreasonable about this result? (c) What…

(a) What is the density of $^{235} \text{U}$ in $\text{u}/\text{fm}^{3}$? (b) If $^{235} \text{U}$ splits into $^{141} \text{Ba}$ and $^{92} \text{Kr} + 3$ neutrons, how does the density of $^{235} \text{U}$ compare with the density of each element it splits into?