Answer
a. $\eta = 7.4\times10^{-11}m$.
b. $\eta = 1.44\times10^{-15}m$.
Work Step by Step
Use the penetration distance formula given in the problem.
a. $\eta = \frac{\hbar}{\sqrt{2m(U_o-E)}}$
$\eta = \frac{1.055\times10^{-34}J \cdot s}{\sqrt{2(9.11\times10^{-31}kg)(20eV-13eV)(1.602\times10^{-19}J/eV)}}$
$\eta = 7.4\times10^{-11}m$
b. $\eta = \frac{\hbar}{\sqrt{2m(U_o-E)}}$
$\eta = \frac{1.055\times10^{-34}J \cdot s}{\sqrt{2(1.67\times10^{-27}kg)(30.0MeV-20.0MeV)(1.602\times10^{-13}J/MeV)}}$
$\eta = 1.44\times10^{-15}m$
