Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 36

How many electron states of the H atom have the quantum numbers \(n=3\) and \(\ell=1 ?\) Identify each state by listing its quantum numbers.

Short Answer

Expert verified
Answer: There are 3 electron states with the quantum numbers \(n=3\) and \(\ell=1\) for hydrogen atom. These states are: \((3, 1, -1)\), \((3, 1, 0)\), and \((3, 1, 1)\).

Step by step solution

01

Find the possible values of the magnetic quantum number \(m_\ell\)

Given that \(\ell = 1\), we can find the possible values of the magnetic quantum number \(m_\ell\) using the range \((-\ell, -\ell+1, ..., 0, ..., \ell-1, \ell)\). So, for \(\ell = 1\), the possible values of \(m_\ell\) will be \((-1, 0, 1)\).
02

Count the number of electron states and identify them

Now that we know the possible values of \(m_\ell\), we can count the number of electron states and identify each state by listing its quantum numbers \((n, \ell, m_\ell)\). There are in total 3 values of \(m_\ell = -1, 0, 1\). The electron states with quantum numbers \((n, \ell, m_\ell)\) are as follows: 1. State 1: \((3, 1, -1)\) 2. State 2: \((3, 1, 0)\) 3. State 3: \((3, 1, 1)\) There are 3 electron states of the hydrogen atom with the given quantum numbers \(n = 3\) and \(\ell = 1\).

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

List the number of electron states in each of the subshells in the \(n=7\) shell. What is the total number of electron states in this shell?
What is the ground-state electron configuration of bromine (Br, atomic number 35)?
In a ruby laser, laser light of wavelength \(694.3 \mathrm{nm}\) is emitted. The ruby crystal is \(6.00 \mathrm{cm}\) long, and the index of refraction of ruby is \(1.75 .\) Think of the light in the ruby crystal as a standing wave along the length of the crystal. How many wavelengths fit in the crystal? (Standing waves in the crystal help to reduce the range of wavelengths in the beam.)
A magnesium ion \(\mathrm{Mg}^{2+}\) is accelerated through a potential difference of \(22 \mathrm{kV}\). What is the de Broglie wavelength of this ion?
An electron moving in the positive \(x\) -direction passes through a slit of width \(\Delta y=85 \mathrm{nm} .\) What is the minimum uncertainty in the electron's velocity in the \(y\) -direction?
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Linear Momentum

Read Explanation

Measurements

Read Explanation

Kinematics Physics

Read Explanation

Rotational Dynamics

Read Explanation

Electric Charge Field and Potential

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