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Consider a potential barrier defined by U(x) = 0 Uo 0 x < 0 0 < x < L x > L with Uo = 1.00 eV. An electron with energy E > 1 eV moving in the positive x- direction is incident on this potential. The transmission probability for this situation is given by

Consider a potential barrier defined by U(x) = 0 Uo 0 x < 0 0 < x < L x > L with Uo = 1.00 eV. An electron with energy E > 1 eV moving in the positive x- direction is incident on this potential. The transmission probability for this situation is given by

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Consider a potential barrier defined by \[ U(x) = \begin{cases} 0 & x < 0 \\ U_0 & 0 < x < L \\ 0 & x > L \end{cases} \] with \( U_0 = 1.00 \text{ eV} \). An electron with energy \( E > 1 \text{ eV} \) moving in the positive \( x \)-direction is incident on this potential. The transmission probability for this situation is given by \[ T = \frac{4(E/U_0)\left[(E/U_0) - 1\right]}{\sin^2\left[\sqrt{2m(E-U_0)}L/\hbar\right] + 4(E/U_0)\left[(E/U_0) - 1\right]}. \] It is found that the reflection probability is zero for \( E = 1.10 \text{ eV} \) and non-zero for smaller incident energies. What is the width of the potential barrier \( L \)?
Transcribed Image Text:Consider a potential barrier defined by \[ U(x) = \begin{cases} 0 & x < 0 \\ U_0 & 0 < x < L \\ 0 & x > L \end{cases} \] with \( U_0 = 1.00 \text{ eV} \). An electron with energy \( E > 1 \text{ eV} \) moving in the positive \( x \)-direction is incident on this potential. The transmission probability for this situation is given by \[ T = \frac{4(E/U_0)\left[(E/U_0) - 1\right]}{\sin^2\left[\sqrt{2m(E-U_0)}L/\hbar\right] + 4(E/U_0)\left[(E/U_0) - 1\right]}. \] It is found that the reflection probability is zero for \( E = 1.10 \text{ eV} \) and non-zero for smaller incident energies. What is the width of the potential barrier \( L \)?
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