# 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.

**Q4: **

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?

**Q5: **

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.

**Q6: **

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.

**Q7: **

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.