Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 36: Problem 39

A hydrogen atom is in an \(l=2\) state. What are the possible angles its orbital angular momentum vector can make with a given axis?

Short Answer

Expert verified
The orbital angular momentum vector can make angles of 0º, 60º, 90º, 120º, and 180º with the given axis.

Step by step solution

01

Calculate the Magnetic Quantum Number Ranges

Given that \(l\) is 2, the magnetic quantum number can range from \(-l\) to \(+l\). Consequently, \(m\) ranges from -2 to +2 with these possible values: -2, -1, 0, 1, 2.
02

Define the Possible Angles

Each of the \(m\) values corresponds to a particular orientation of the orbital, and thus a particular angle \(\theta\), the angle that the orbital angular momentum vector makes with the z-axis. These angles \(\theta\) can be found using the relation \(\cos(\theta) = m/l\). Compute these values by using the obtained \(m\) values from Step 1.
03

Determine the Angular Measurements

The angles associated with the \(m\) values, in ascending order, are \(acos(-2/2) = 180^\circ~, acos(-1/2) = 120^\circ~, acos(0/2) = 90^\circ~, acos(1/2) = 60^\circ~, acos(2/2) = 0^\circ\).

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

Adapt part (b) of Example 36.1 to find the probability that an electron in the hydrogen ground state will be found beyond two Bohr radii.

Write the full electronic structure of scandium.

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.

Write the full electronic structure of bromine.

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

Radiation

Read Explanation

Mechanics and Materials

Read Explanation

Force

Read Explanation

Modern Physics

Read Explanation

Solid State Physics

Read Explanation

Thermodynamics

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