Part A: What is the energy of the system when in its ground state, in units of eV? ### Quantum Mechanics: Particle in a Box#### Diagram DescriptionThe diagram illustrates a one-dimensional potential energy well (also known as an infinite potential well), which is represented by a box with infinitely high walls. The potential energy \( U \) is indicated by two vertical arrows pointing upwards at \( x = 0 \) and \( x = L \), suggesting infinite potential at these boundaries. The region between these points (from 0 to L on the x-axis) is where the particle, in this case, a neutron, is confined.#### System DescriptionA neutron is trapped in a one-dimensional box of length \( L = 2.00 \times 10^{-11} \) meters, with walls of infinite potential energy. This means that the neutron cannot exist outside the defined region between the walls. The rest mass of the neutron is given as \( 1.68 \times 10^{-27} \) kilograms. Initially, the neutron is in its ground state configuration, which is its lowest energy state. Upon interacting with a photon, the neutron absorbs energy and is excited to a higher energy level, specifically to the state \( n = 2 \). This process exemplifies quantum excitation, where the energy absorbed from the photon causes the neutron to "jump" to a higher energy state within its confined environment.

The energy can be calculated by the following formula. E=n2h28mL2E=energyn=energy levelh=planck's…

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What is the energy of the system when in its ground state, in units of eV?

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter12: Atoms And Molecules

Section: Chapter Questions

Problem 12.12E: Are mathematical expressions for the following potential energies positive or negative? Explain why...

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Question

Part A: What is the energy of the system when in its ground state, in units of eV?

### Quantum Mechanics: Particle in a Box

#### Diagram Description
The diagram illustrates a one-dimensional potential energy well (also known as an infinite potential well), which is represented by a box with infinitely high walls. The potential energy \( U \) is indicated by two vertical arrows pointing upwards at \( x = 0 \) and \( x = L \), suggesting infinite potential at these boundaries. The region between these points (from 0 to L on the x-axis) is where the particle, in this case, a neutron, is confined.

#### System Description
A neutron is trapped in a one-dimensional box of length \( L = 2.00 \times 10^{-11} \) meters, with walls of infinite potential energy. This means that the neutron cannot exist outside the defined region between the walls. The rest mass of the neutron is given as \( 1.68 \times 10^{-27} \) kilograms. Initially, the neutron is in its ground state configuration, which is its lowest energy state.

Upon interacting with a photon, the neutron absorbs energy and is excited to a higher energy level, specifically to the state \( n = 2 \). This process exemplifies quantum excitation, where the energy absorbed from the photon causes the neutron to "jump" to a higher energy state within its confined environment.

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