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

Question

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Answer 1

Question

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

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Answer 2

Question

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

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Answer 3

Question

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

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Answer 4

Question

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

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Answer 5

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

Answer 6

Chapter 41, Problem 1OQ

To determine

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

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

Answer 7

Chapter 41, Problem 1OQ

To determine

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

Answer 8

Expert Solution & Answer

Answer to Problem 1OQ

Option (b), It decreases.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Write the expression for the transmission coefficient.

$T≈e−22m(U−E)Lℏ$ (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, $ℏ$ 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 $(U−E)$ . 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.

Answer 12

Ch. 41.1 - Prob. 41.1QQ Ch. 41.2 - Prob. 41.2QQ Ch. 41.2 - Prob. 41.3QQ Ch. 41.5 - Prob. 41.4QQ Ch. 41 - Prob. 1OQ Ch. 41 - Prob. 2OQ Ch. 41 - Prob. 3OQ Ch. 41 - Prob. 4OQ Ch. 41 - Prob. 5OQ Ch. 41 - Prob. 6OQ

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

The change in fraction of the particles that are reflected changes as the barrier height is reduced to 2.01 eV<m:math><m:mrow><m:mn>2.01</m:mn><m:mtext> eV</m:mtext></m:mrow></m:math> .

Answer to Problem 1OQ

Explanation of Solution

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Chapter 41 Solutions

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