Problem 82
The first nuclear reaction ever observed (in 1919 by Ernest Rutherford) was
\(\alpha+_{7}^{14} \mathrm{N} \right arrow \mathrm{p}+\mathrm{X} .\) (a) Show
that the reaction product "X" must be \(\quad\) 8O. (b) For this reaction to
take place, the \(\alpha\) particle must come in contact with the nitrogen
nucleus. Calculate the distance \(d\) between their centers when they just make
contact.
(c) If the \(\alpha\) particle and the nitrogen nucleus are initially far apart,
what is the minimum value of their kinetic energy necessary to bring the two
into contact? Express your answer in terms of the elementary charge \(e\), the
contact distance \(d\), and whatever else you need. (d) Is the total kinetic
energy of the reaction products more or less than the initial kinetic energy
in part (c)? Why? Calculate this kinetic energy difference.
Problem 83
The last step in the carbon cycle that takes place inside stars is
\(\mathrm{p}+^{15} \mathrm{N} \rightarrow^{12} \mathrm{C}+(?) .\) This step
releases \(5.00 \mathrm{MeV}\) of energy. (a) Show that the reaction product
"(?)" must be an \(\alpha\) particle. (b) Calculate the atomic mass of helium-4
from the information given. (c) In order for this reaction to occur, the
proton must come into contact with the nitrogen nucleus. Calculate the
distance \(d\) between their centers when they just "touch." (d) If the proton
and nitrogen nucleus are initially far apart, what is the minimum value of
their total kinetic energy necessary to bring the two into contact?
