20. an electron with total energy 5 ev approaches a potential barrier of height 20 ev. if the probability that the electron tunnels across the barrier is 0.03, what is the width l of the barrier? a. 0.0116 nm b. 0.116 nm c. 1.16 nm d. 11.6 nm e. 116 nm spring 2009 21. define k ue

The width L of the barrier is b. 0.116nm

Explanation:

This is a case of tunnel effect when the probability is less than one.

First of all you find all the information the problem gives you:

Electron's total energy E=5eV

Height of potential barrier U=20eV

Crossing Probability T=0.03

Width of the barrier L=unknown

Then you need to find the equations to use in cases in which the probability is less than 0, so you have:

where m is the mass of the electron, , and h is the Planck constant,

First we find G, we have:

Now, to solving k, we need to find the difference (U-E) :

U - E = 20eV - 5eV = 15eV

Then, we can find k:

Finally, we solve for L the probability equation T:

And replacing values for T, G and k, we can find the width of the barrier:

L=0.116nm

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