An electron with kinetic energy 2.80 eV encounters a potential barrier of height 4.70 eV. If the barrier width is 0.40 nm, what is the probability that the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

Question

Quizplus · Accepted Answer

The probability of tunneling can be calculated using the formula for the transmission coefficient T ≈ e^(-2 * k * a), where k = sqrt((2 * m * (V - E)) / ħ^2), m is the electron mass, V is the barrier height, E is the electron energy, a is the barrier width, and ħ is the reduced Planck's constant. Substituting the given values, the probability is approximately 1.4 × 10^-2.

An Electron with Kinetic Energy 2