Chapter 41, Problem 1OQ

To determine

The change in fraction of the particles that are reflected changes as the barrier height is reduced to $2.01\text{ eV}$ .

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

   $T\approx e^{-2\sqrt{2m\left(U-E\right)}\frac{L}{\hslash }}$                                                                                                       (I)

Here, $T$ is the transmission coefficient, $m$ is the mass of the particle, $U$ is the height of the potential barrier, $E$ is the energy of the particles, $\hslash$ is the reduced Planck’s constant and $L$ is the width of the potential barrier.

Write the equation for the reflection coefficient.

  $R=1-T$                                                                                                             (II)

Here, $R$ is the reflection coefficient.

When the barrier height is reduced, the difference between the barrier height and the energy of the particles decreases. According to equation (I), T increases with decrease in $\left(U-E\right)$ . According to equation (II), with increase in transmission coefficient, reflection coefficient decreases.

Conclusion:

Since reflection coefficient decreases with decrease in potential barrier, option (b) is correct.

Since the reflection coefficient decreases with decrease in potential barrier, option (a) is incorrect.

Since the reflection coefficient changes with decrease in potential barrier, option (c) is incorrect.

Since the reflection coefficient changes with decrease in potential barrier, option (d) is incorrect.

Since the reflection coefficient changes with decrease in potential barrier, option (e) is incorrect.