Question

Showed that a typical nuclear radius is $4fm$ As you’ll learn in Chapter 42, a typical energy of a neutron bound inside the nuclear potential well is$E_n=-20MeV$. To find out how “fuzzy” the edge of the nucleus is, what is the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius?

Short answer

^{The neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius is$1.02fm$.}

Step-by-step solution

Given Information

We need to find the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius.

Simplify

The distance $\eta$is given as the equation:

$\eta =\frac{h}{\sqrt{2m\left(U_0-E\right)}}$

Since the neutron's energy is $20MeV$under $U_0$, so the $\left(U_0-E\right)$has a value of $20MeV$, and the distance is:

$$\begin{gathered} \eta =\frac{1.05\times {10}^{-34}Js}{\sqrt{2\left(1.67\times {10}^{-27}kg\right)\left(20\times {10}^{6}eV\times 1.6\times {10}^{-19}{\displaystyle \raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$eV$}\right.}\right)}} \\ \eta =1.2\times {10}^{-15}m=1.02fm \end{gathered}$$

The penetration distance is $25\%$of the nuclear radius.