Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 36: Problem 16

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

Short Answer

Expert verified
The maximum possible magnitude of the orbital angular momentum for an electron in the \(n=7\) state of hydrogen = \(\sqrt{42}\hbar\).

Step by step solution

01

Identify the value of the principal quantum number

The principal quantum number 'n' is given in the problem statement. In this case, 'n' is equal to 7.
02

Calculate the azimuthal quantum number 'l'

The azimuthal quantum number 'l' is equal to n-1. Here, since 'n' is 7, 'l' equals 7 - 1 = 6.
03

Use the angular momentum formula

Substitute the azimuthal quantum number 6 into the formula for the magnitude of the angular momentum \[L=\sqrt{l(l+1)}\hbar \]. Computing, we get \[L=\sqrt{6(6+1)}\hbar =\sqrt{42}\hbar\].
04

Simplify the expression

Simplifying the result, we are left with the final answer for the maximum possible magnitude of the orbital angular momentum.

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

Can the component of a quantized angular momentum measured on a given axis ever equal the magnitude of the angular momentum vector? Explain.

How many quantum numbers are required to specify fully the state of a hydrogen atom?

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

Helium and lithium exhibit very different chemical behavior, yet they differ by only one unit of nuclear charge. Explain.

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

Magnetism and Electromagnetic Induction

Read Explanation

Medical Physics

Read Explanation

Physical Quantities And Units

Read Explanation

Nuclear Physics

Read Explanation

Mechanics and Materials

Read Explanation

Energy 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