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Chapter 36: Problem 1

The electron in a hydrogen atom is somewhat like a particle confined to a three-dimensional box. In the atom, what plays the role of the confining box?

Short Answer

Expert verified
In a hydrogen atom, the 'confining box' is the electrostatic attraction between the proton and the electron, which confines the electron and creates an electron cloud.

Step by step solution

01

Understanding the Structure of the Atom

A hydrogen atom consists of a single electron orbiting a single proton. According to quantum mechanics, the electron does not move in a defined orbit but rather exists in an electron cloud around the nucleus.
02

Comparing Atom Structure to a Confining Box

When the electron in a hydrogen atom is likened to a particle confined in a three-dimensional box, it refers to the electron's constrained movement within the electron cloud. In this case, the term 'confining box' refers to the electron cloud that confines or limits the electron's movement.
03

Identifying the Confining Factor

In a hydrogen atom, what plays the role of the confining box is the electrostatic attraction force between the positively charged proton in the nucleus and the negatively charged electron. This force confines the electron, keeping it within a certain distance from the nucleus and preventing it from escaping, thereby creating an 'electron cloud' or 'confining box'.

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Most popular questions from this chapter

The \(4 f \rightarrow 3 p\) transition in sodium produces a spectral line at \(567.0 \mathrm{nm} .\) Find the energy difference between these two levels.

Give a symbolic description for the state of the electron in a hydrogen atom with total energy -1.51 eV and orbital angular morentum \(\sqrt{6} \hbar.\)

Emission of characteristic \(\mathrm{X}\) rays occurs in the context of multielectron atoms that generally have all but one of their electrons present. You should therefore expect the X-ray energies to be described a. quite accurately by Bohr's atomic theory. b. through hydrogen-like solutions to the Schr枚dinger equation. c. only approximately by Bohr's theory or hydrogenic solutions to the Schr枚dinger equation.

(a) Verify Equation 36.8 by considering a single-electron atom with nuclear charge \(Z e\) instead of \(e\). (b) Calculate the ionization energies for single- electron versions of helium, oxygen, lead, and uranium.

What are the possible \(j\) values for a hydrogen atom in the \(3 D\) state?
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