An electron of energy E = eV is incident on a barrier of width L = nm and height V_o = eV as shown in the figure below. (In the figure E is shown correctly to be less than V_o, but the relative magnitudes of E and V_o may not be shown correctly.) In doing this question, ignore the prefactor in the formula you were given in lecture for the tunneling probability. Just use the exponential part of T (see the "useful equations" link below).

a) What is the probability that the electron will pass through the barrier?

The transmission probability is .

b) By how much would the energy of the electron have to increase for the transmission probability to increase by a factor of 10? (The answer is a positive number.)

The increase in the electron energy is eV.

c) By how much would the width of the well have to decrease for the transmission probability to increase by a factor of 10? (The answer is a positive number.)

The decrease in the width of the well is nm.