= Solution
Here the step is upward by $U=3\,\mathrm{eV}$, so the forbidden-region energy difference is $U-E=1\,\mathrm{eV}$. The bounded wavefunction is
$$
\psi_>(x)=Ce^{-\kappa x},\qquad
\kappa=\frac{\sqrt{2m(U-E)}}{\hbar}.
$$
The requested \b[amplitude] penetration depth is $\delta=1/\kappa$. Using the supplied mass and $h$,
$$
\boxed{\delta=\frac{6.63\times10^{-34}/(2\pi)}{\sqrt{2(9.11\times10^{-31})(1.60218\times10^{-19})}}
=1.95\times10^{-10}\,\mathrm m=0.195\,\mathrm{nm}.}
$$
The probability density decays as $e^{-2\kappa x}$, so its $1/e$ depth is half this value. For an ideal lossless semi-infinite step below threshold, the evanescent tail does not imply net stationary particle current deep into the material; the reflected flux is unity.
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