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.

Q1:

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 7.00 eV.

Q2:

An electron with initial kinetic energy 32.0 eV encounters a square potential barrier with height 41.0 eV and width 0.250 nm. Find the probability, as a percentage, that the electron will tunnel through this barrier.

Q3:

An electron with kinetic energy 2.0 MeV encounters a potential energy barrier of height 16.0 MeV and width 2.00 nm. What is the probability that the electron emerges on the other side of the barrier?

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 𝑒 2 𝛽 𝐿 , where 𝛽 = 1 0 . 0 n m 1 and 𝐿 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 3 . 0 0 % . Find the width of the barrier.

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