/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 A particle is confined to a 1.0 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 35: Problem 21

A particle is confined to a 1.0 -nm-wide infinite square well. If the energy difference between the ground state and the first excited state is \(1.13 \mathrm{eV},\) is the particle an electron or a proton?

Short Answer

Expert verified
The particle is likely to be an electron, but this conclusion should be confirmed by comparing the given energy difference with a calculated one based on the particle being an electron. If the calculated difference is higher than the given value, then the particle is indeed an electron. The reverse applies, too: if the calculated difference is lower, the particle could be a proton.

Step by step solution

01

Converting energy difference to Joules

First, we convert the given energy difference from eV (Electron-Volts) to Joules (J) using the conversion factor \(1 eV = 1.602 脳 10^{-19} J\). This gives us \(1.13 eV 脳 1.602 脳 10^{-19} J/eV = 1.8106 脳 10^{-19} J\).
02

Calculating number for electron in ground state and first excited state

Using the energy equation \(E = \frac{{n^2h^2}}{{8mL^2}}\), we substitute the values \(n = 1\) for ground state, and \(n = 2\) for first excited state. Note that the mass \(m\) will be the mass of an electron because we are currently trying to test for the electron case. Substituting the mass of an electron = \(9.11 脳 10^{-31} kg\), Planck's constant \(h = 6.63 脳 10^{-34} Js\), and \(L = 1nm = 1 脳 10^{-9} m\), we calculate the energy difference \(\Delta E = E_2 - E_1\) where \(E_2\) and \(E_1\) are the energies for \(n=2\) and \(n=1\) respectively.
03

Comparing calculated and given energy differences

After the calculation in Step 2, we compare the computed energy difference with the given energy difference (already converted to Joules). If the computed energy difference is higher than the given value, it indicates the particle is an electron because a lighter particle (like electron) will have higher energy difference than a heavy particle (like proton) occupying the same energy levels. If the computed energy difference is lower, it would imply the particle is a proton.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The ground-state energy of a harmonic oscillator is 4.0 eV. Find the energy separation between adjacent quantum states.

Explain qualitatively why a particle confined to a finite region cannot have zero energy.

One reason we don't notice quantum effects in everyday life is that Planck's constant \(h\) is so small. Treating yourself as a particle (mass \(60 \mathrm{kg}\) ) in a room-sized one-dimensional infinite square well (width \(2.6 \mathrm{m}\) ), how big would \(h\) have to be if your minimum possible energy corresponded to a speed of \(1.0 \mathrm{m} / \mathrm{s} ?\)

What did Einstein mean by his remark, loosely paraphrased, that "God does not play dice"?

A particle is in the ground state of an infinite square well. What's the probability of finding the particle in the left-hand third of the well?
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Thermodynamics

Read Explanation

Turning Points in Physics

Read Explanation

Magnetism

Read Explanation

Medical Physics

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.