Worksheet: Quantum Tunneling through Potential Barriers
In this worksheet, we will practice calculating the probability that a particle will tunnel through a potential barrier with energy exceeding that of the particle.
In scanning-tunneling microscopy (STM), tunneling-electron current is in direct proportion to the tunneling probability and tunneling probability is to a good approximation expressed by the function , where and is the distance of the tip of the scanning-tunneling microscope from the surface being scanned. If STM is used to detect surface features with heights of 0.00200 nm, what percent change in tunneling-electron current must the STM electronics be able to detect?
An electron with an energy of 5.0 eV impacts on a barrier of width 0.30 nm. Find the probability that the electron will tunnel through the barrier if the barrier height is 9.0 eV.
An electron with an energy of 5.0 eV impacts on a barrier of width 0.30 nm. Find the probability that the electron will tunnel through the barrier if the barrier height is 13.0 eV.
A 13.0 eV electron encounters a barrier with a height of 16.0 eV. The probability of the electron tunneling through the barrier is . Find the width of the barrier.