Whether the probability that the particle will tunnel through a given barrier increase, decrease or stay same if the de Broglie wavelength of a particle is increased.

Question

Want to see the full answer?

Answer 1

Question

Chapter 30.7, Problem 7EYU

To determine

Whether the probability that the particle will tunnel through a given barrier increase, decrease or stay same if the de Broglie wavelength of a particle is increased.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

When low-energy electrons pass through an ionized gas, electrons of certain energies pass through the gas as if the gas atoms weren’t there and thus have transmission coefficients (tunneling probabilities) T equal to unity. The gas ions can be modeled approximately as a rectangular barrier. The value of T = 1 occurs when an integral or half-integral number of de Broglie wavelengths of the electron as it passes over the barrier equal the width L of the barrier. You are planning an experiment to measure this effect. To assist you in designing the necessary apparatus, you estimate the electron energies E that will result in T = 1. You assume a barrier height of 10 eV and a width of 1.8 x 10-10 m. Calculate the three lowest values of E for which T = 1

A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d. Even though U >> E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decrease to 0.12 d, what percentage of the electrons will tunnel through?

The wavefunction for a quantum particle tunnelling through a potential barrier of thickness L has the form ψ(x) = Ae−Cx in the classically forbidden region where A is a constant and C is given by C^2 = 2m(U − E) /h_bar^2 . (a) Show that this wavefunction is a solution to Schrodinger’s Equation. (b) Why is the probability of tunneling through the barrier proportional to e ^−2CL?