Skip to main content
Ch 40: One-Dimensional Quantum Mechanics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 40: One-Dimensional Quantum MechanicsProblem 32b
Chapter 40, Problem 32b

A particle confined in a rigid one-dimensional box of length 10 fm has an energy level En = 32.9 MeV and an adjacent energy level En+1 = 51.4 MeV. Draw an energy-level diagram showing all energy levels from 1 through n+1. Label each level and write the energy beside it.

Verified step by step guidance
1
Step 1: Understand the problem. The particle is confined in a rigid one-dimensional box, which means its energy levels are quantized. The energy levels are given by the formula: E=n2⋅h2⋅pi........

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quantum Mechanics

Quantum mechanics is the branch of physics that deals with the behavior of particles at the atomic and subatomic levels. It introduces concepts such as quantization of energy levels, where particles can only occupy specific energy states. This is crucial for understanding how a particle in a one-dimensional box can have discrete energy levels, as described by the Schrödinger equation.
Recommended video:
Guided course
06:24
Conservation Of Mechanical Energy

Particle in a Box Model

The particle in a box model is a fundamental quantum mechanics problem that illustrates how a particle confined to a rigid, one-dimensional box can only have certain allowed energy levels. The energy levels are determined by the length of the box and the mass of the particle, leading to quantized states. This model helps visualize the concept of confinement and energy quantization in quantum systems.
Recommended video:
Guided course
04:27
Power of Pushing a Box

Energy Level Diagram

An energy level diagram is a graphical representation of the quantized energy levels of a system, typically arranged vertically with energy values indicated. Each level corresponds to a specific state of the particle, and transitions between levels can represent absorption or emission of energy. In this context, drawing the diagram for the particle in a box will help visualize the energy levels from 1 through n+1, including their respective energies.
Recommended video:
Guided course
08:07
Work and PV Diagrams
Related Practice
Textbook Question

INT Model an atom as an electron in a rigid box of length 0.100 nm, roughly twice the Bohr radius. Calculate all the wavelengths that would be seen in the emission spectrum of this atom due to quantum jumps between these four energy levels. Give each wavelength a label λn→m to indicate the transition.

Textbook Question

A particle confined in a rigid one-dimensional box of length 10 fm has an energy level En = 32.9 MeV and an adjacent energy level En+1 = 51.4 MeV. What is the mass of the particle? Can you identify it?

1
views
Textbook Question

A particle confined in a rigid one-dimensional box of length 10 fm has an energy level En = 32.9 MeV and an adjacent energy level En+1 = 51.4 MeV. Sketch the n+1 wave function on the n+1 energy level.

1
views
Textbook Question

CALC Consider a particle in a rigid box of length L. For each of the states n = 1,n = 2, and n = 3: Where, in terms of L, are the positions at which the particle is most likely to be found?

1
views
Textbook Question

INT Model an atom as an electron in a rigid box of length 0.100 nm, roughly twice the Bohr radius. What are the four lowest energy levels of the electron?

2
views
Textbook Question

A particle confined in a rigid one-dimensional box of length 10 fm has an energy level En = 32.9 MeV and an adjacent energy level En+1 = 51.4 MeV. Determine the values of n and n+1.

1
views