Question

Electrons are fired at a rectangular potential energy barrier, once every 245 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 537 meV, how long on average would you expect to wait for one electron to pass through the barri Number seconds

Answer 1

Given data: Electrons are Fixed at a rectangular Potential Energy barrier, once every - 245 ms. Barrier thickness - 2.55 nm Incident electrons exactly - 531 mev we have to find the how long on average would you expect to wait for one electron to pass through the barrier T = e^-2 squareroot m (V - E)/h^2 L squareroot M(V - E)/h^2 = squareroot (9.1 times 10^31) times (537 times 10^-3 times 1.6 times 10^-19)/ (1.055 times 10^-34)^2 = squareroot 7.0247478 times 10^8 = 2.65 times 10^9 T = e^-[- 2 times (2.65 times 10^9) times (2.55 times 10^-9)] = 1.35 times 10^-7 Tunneling Probability per attempt = 1.35 times 10^-7 So total of 1/(1.35 times 10^-7) attempts need o be made = 7.40 times 10^6 electrons need to hit the potential Barrier. Time taken = 7.40 times 10^6 times 0.245 = 18.13 times 10^5 S