The energy of the electron in the given region is 9.38 eV.
The given parameters:
When a particle of energy E less than the potential cannot penetrate inside that region.
The exponential factor is calculated as follows;
[tex]T = e^{-2 \alpha a} \\\\ 0.008 = e^{-2(0.6 \times 10^{-9})\alpha}\\\\ -2(0.6 \times 10^{-9})\alpha = ln(0.008)\\\\ -2(0.6 \times 10^{-9})\alpha = -4.828\\\\ \alpha = \frac{-4.828}{-2(0.6 \times 10^{-9})} \\\\ \alpha = 4.023 \times 10^9[/tex]
The energy of the electron is calculated as follows;
[tex]\alpha = \sqrt{\frac{2m(U_0 -E)}{h^2} } \\\\ 4.023 \times 10^9 = \sqrt{\frac{2 ( 9.11 \times 10^{-31} kg)(10 \ eV -E) \ \times 1.6\times 10^{-19} \ J/eV}{(1.055 \times 10^{-34} \ J.s)^2 } } \\\\ (4.023 \times 10^9)^2 = \frac{2 ( 9.11 \times 10^{-31} kg)(10 \ eV -E) \ \times 1.6\times 10^{-19} \ J/eV}{(1.055 \times 10^{-34} \ J.s)^2 }\\\\ 2 ( 9.11 \times 10^{-31} )(10 \ eV -E) 1.6\times 10^{-19} = (4.023 \times 10^9)^2 (1.055 \times 10^{-34} \ )^2\\\\ [/tex]
[tex]10eV - E = \frac{(4.023 \times 10^9)^2\times (1.055 \times 10^{-34} \ )^2}{2 ( 9.11 \times 10^{-31} ) \times 1.6\times 10^{-19}} \\\\ 10eV - E = 0.62 \ eV\\\\ E = 10 \ eV - 0.62\ eV\\\\ E = 9.38 \ eV[/tex]
Thus, the energy of the electron in the given region is 9.38 eV.
Learn more about electron barrier penetration here: https://brainly.com/question/5838250
