Please show all the work. thank you! An electron with kinetic energy E = 4.00 eV

Question

Please show all the work. thank you!

An electron with kinetic energy E = 4.00 eV is incident on a barrier of width L = 0.170 nm and height U = 10.0 eV. what is the probability that the electron tunnels through the barrier? (Use 9.11 times 10^-31 kg for the mass of an electron, 1.055 times 10^-34 J. s for h, and note that there are 1.60 times 10^-19 J per ev.) What is the expression for the transmission coefficient that corresponds to low transmission probability? How can you determine if this is an appropriate expression for this case? What is the probability that the electron is reflected?

Explanation / Answer

a)

here by using the formula

A = 16 *( E / U0) * (1 - E/U0)

A = 16 * (4 / 10) * (1 - 4 / 10 )

A = 3.84

then

K = sqrt(2*m*(U0 - E)/h)

K = sqrt((2 * 9.11 * 10^-31(10 -4) * 1.60 * 10^-19) / (1.055 * 10^-34))

K = 1.25 * 10^10 m^-1

then

T = A * e^-(2*K*L)

T = 3.84 * e^-2*(1.288 * 10^10 * 0.17*10-9)

T = 0.0547

b)

then the probability of the electron being reflected will be 1 - T = 1 - 0.0547 = 0.9453

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