Chapter 6: Q10E (page 1354)

A proton is in a box of width L . What must the width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus-that is, on the order of $10^{14} m$ .

Short Answer

Expert verified

The width of the box be $0.641 \times 10^{- 14} M$ for the ground level energy to be 5.0 MeV , a typical value for the energy with which the particles in a nucleus are bound and the order of width is same as the diameter of the nucleus.

Step by step solution

Define the energy level.

The energy level of a particle of mass in a box of width is:

$E_{n} = \frac{P_{n}^{2}}{2 m} = \frac{n^{2} h^{2}}{8 m L^{2}} = \frac{n^{2} π^{2} h^{2}}{2 m L^{2}} (n = 1, 2, 3, . . .)$

Determine the width of box.

Given that, energy $E_{1}$ of photon at ground level is 5.0 MeV .

The energy $E_{1}$ in joule is J

$E_{1} = 5.00 \times (\frac{1.60 \times 10^{- 13}}{1}) = 8.00 \times 10^{- 13} J$

The mass of photon is $1.67 \times 10^{- 27} k g$ and value of $h = 1.055 \times 10^{- 34} J . s$ .

The width of the box is:

$L = \frac{n πh}{\sqrt{2 m E_{n}}} = \frac{(1) π (1.055 \times 10^{- 13})}{\sqrt{2 (1.67 \times 10^{- 27}) (8.00 \times 10^{- 13})}} = 0.641 \times 10^{- 14} m$

Hence, the width of the box is $0.641 \times 10^{- 14} m$ and order of width is same as the diameter of the nucleus.

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.

A proton is in a box of width L . What must the width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus-that is, on the order of $10^{14} m$ .

Short Answer

Step by step solution

Define the energy level.

Determine the width of box.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Thermodynamics

Electrostatics

Energy Physics

Kinematics Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

A proton is in a box of width L . What must the width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus-that is, on the order of1014m .

Short Answer

Step by step solution

Define the energy level.

Determine the width of box.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Thermodynamics

Electrostatics

Energy Physics

Kinematics Physics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

A proton is in a box of width L . What must the width of the box be for the ground level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus-that is, on the order of $10^{14} m$ .