Chapter 40: Q. 9 (page 1174)

An electron has a $0.0100$ probability (a $1.00 %$ chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be $0.0050, 0.0025 o r 0.0001$ ? Explain.

Short Answer

Expert verified

The width of the barrier is doubled , will the tunneling probability be $0.0050, 0.0025 o r 0.0001$ is $P_{t u n n e l, 2} = 0.0001$ .

Step by step solution

Given Information

We have to given that an electron has a $0.0100$ , the width of the barrier is doubled, will the tunneling probability be $0.0050, 0.0025 o r 0.0001$ .

Simplify

$P_{t u n n e l, 2} =$ The probability that the electron is the tunnel through the barrier is given as the equation:

$P_{t u n n e l} = e^{\frac{- 2 ω}{η}}$

and we are given that the initial probability is $(0.01)$ , so let the probability after the width of the barrier is doubled be $P_{t u n n e l, 2}$ since:

$ω_{1}$ is the initial width after doubling. Notice that $e^{a b} = {(e^{a})}^{b}$ . Then:

role="math" localid="1650132194389" $P_{t u n n e l, 2} = e x p (- \frac{4 ω_{1}}{η}) = e x p {(- \frac{2 ω_{1}}{η})}^{2} = {(P_{t u n n e l, 1})}^{2} P_{t u n n e l, 2} = 0.0001$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

An electron has a $0.0100$ probability (a $1.00 %$ chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be $0.0050, 0.0025 o r 0.0001$ ? Explain.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Electromagnetism

Electrostatics

Oscillations

Wave Optics

Waves Physics

Study anywhere. Anytime. Across all devices.

An electron has a 0.0100 probability (a 1.00% chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be0.0050,0.0025or0.0001? Explain.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Electromagnetism

Electrostatics

Oscillations

Wave Optics

Waves Physics

Study anywhere. Anytime. Across all devices.

An electron has a $0.0100$ probability (a $1.00 %$ chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be $0.0050, 0.0025 o r 0.0001$ ? Explain.