Tunneling: An 80-eV electron impinges upon a potential barrier 100 eV high and 0.20 nm thick. What is the probability the electron will tunnel through the barrier? (1 eV = 1.60 × 10^-19 J, m_proton = 1.67 × 10^-27 kg, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s) A) 0.027% B) 2.7% C) 0.27% D) 2.8 × 10^-4 % E) 2.0 × 10^-9 %

Question

Quizplus · Accepted Answer

The tunneling probability can be calculated using the formula: T ≈ e^(-2 * κ * a), where κ = sqrt((2 * m * (V - E)) / ħ²), m is the electron mass (9.11 × 10^-31 kg), V is the barrier height (100 eV), E is the electron energy (80 eV), and a is the barrier width (0.20 nm). After calculating κ and substituting the values, the tunneling probability is approximately 0.00027 or 0.027%.

Tunneling: an 80-EV Electron Impinges Upon a Potential Barrier 100