Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 36: Problem 9

Why is there no spin-orbit splitting in hydrogen's ground state?

Short Answer

Expert verified
There is no spin-orbit splitting for Hydrogen's ground state because spin-orbit interaction only occurs significantly in atoms/ions with multiple electrons. Hydrogen only has one. Furthermore, Hydrogen's ground state (1s orbital) has zero orbital angular momentum, a key requirement for the existence of spin-orbit interaction.

Step by step solution

01

Understanding Spin-Orbit Interaction

The spin–orbit interaction (SOI) is a magnetic interaction of a particle's spin with its motion. Specifically, it describes the energy changes due to magnetic interaction between the angular momentum and the spin of the electron. However, this interaction is only significant in atoms/ions with multiple electrons.
02

Knowing Hydrogen's Ground State

The ground state of a hydrogen atom is where the atom's electron is in the lowest possible energy level. This state is known as a 1s orbital. The 's' in 1s means that state has zero orbital angular momentum.
03

Combining the Facts

Given the above observations, in a Hydrogen atom's ground state (1s), there is no spin orbit coupling because the orbital has zero angular momentum. Furthermore, Hydrogen is a one-electron ion, and the central field in such ions is spherically symmetric. Thus, breaking the field's spherical symmetry by the motion of an electron around the nucleus, the basis of spin-orbit interaction, does not occur. Hence, there is no spin-orbit splitting in Hydrogen's ground state.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

How does the Stern-Gerlach experiment provide convincing evidence for space quantization?

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?

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

Find the maximum possible magnitude for the orbital angular momentum of an electron in the \(n=7\) state of hydrogen.

A hydrogen atom is in the \(2 s\) state. Find the probability that its electron will be found (a) beyond one Bohr radius and (b) beyond 10 Bohr radii.
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Kinematics Physics

Read Explanation

Astrophysics

Read Explanation

Torque and Rotational Motion

Read Explanation

Medical Physics

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.

Sign-up for free