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For three experiments, Fig. 38-25 gives the transmission coefficient T for electron tunneling through a potential barrier, plotted versus barrier thickness L. The de Broglie wavelengths of the electrons are identical in the three experiments. The only difference in the physical setups is the barrier heights Ub. Rank the three experiments according to Ubgreatest first.

Short Answer

Expert verified

The rank is U3>U2>U1.

Step by step solution

01

Describe the expression for probability of electron:

The probability that is given by the transmission coefficient T is as follows.

T=e-2bL, where b=82m(U-E)h2

Here, U is barrier of height and L is the thickness.

According to these equations, the transmission coefficient decreases as the potential height increases and also decreases as the energy of the incident beam decreases, it can be observed that, it depends on the value of U-Eincreases the transmission coefficient decrease. Also, the transmission coefficient depends on width of the barrier, so,

Te-LU-E

02

Rank the three experiments:

From the graph, it can be observed that the graph between L and T is a decreasing exponential. It is known that the curve with a greater values have the smaller factor in the exponential, since the only difference is in the barrier height, then the curve with the higher barrier height has a smaller values of T , therefore the rank of the potential step height is U3>U2>U1.

Hence, the rank is U3>U2>U1.

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