   Chapter 10, Problem 10.51E

Chapter
Section
Textbook Problem

How many nodes are there for the one-dimensional particle-in-a-box in the state described by Ψ 5 ? by Ψ 10 ? by Ψ 100 ? Do not include the sides of the box as nodes.

Interpretation Introduction

Interpretation:

The number of nodes for the one-dimensional particle-in-a-box in the state described by Ψ5, Ψ10 and Ψ100 are to be stated.

Concept introduction:

The number of nodes for the one-dimensional particle-in-a-box in the state described as the position where probability of finding the electron is zero. These nodes do not include the boundary positions. At the node, the wavefunction gives a value of zero.

Explanation

The number of nodes for the one-dimensional particle-in-a-box having wave function Ψn is given as (n1). Therefore, for the given functions, the numbers of nodes are as follows.

For Ψ5, number of nodes is (51)=4

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