The three lowest value of E for which T = 1 .

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Chapter 40, Problem 40.63P

To determine

The three lowest value of E for which T=1.

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When low-energy electrons pass through an ionized gas, electrons of certain energies pass through the gas as if the gas atoms weren’t there and thus have transmission coefficients (tunneling probabilities) T equal to unity. The gas ions can be modeled approximately as a rectangular barrier. The value of T = 1 occurs when an integral or half-integral number of de Broglie wavelengths of the electron as it passes over the barrier equal the width L of the barrier. You are planning an experiment to measure this effect. To assist you in designing the necessary apparatus, you estimate the electron energies E that will result in T = 1. You assume a barrier height of 10 eV and a width of 1.8 x 10-10 m. Calculate the three lowest values of E for which T = 1

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