Chapter 41: Q. 7 (page 1207)

When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with $n = 1$ ? With $n = 2$ ? With $n = 3$ ? List the quantum numbers of each state.

Short Answer

Expert verified

The quantum states are there for a hydrogen atom with $n = 1$ is $2$ states, $n = 2$ is $8 s t a t e s$ and $n = 3$ is $18$ states.

Step by step solution

Given Information

We need to find different quantum states are there for a hydrogen atom with $n = 1, n = 2$ and $n = 3$ .

Simplify

We finding a list of the quantum numbers of each state.
We know that, the two electrons have a set of quantum numbers $(n, l, m, m_{s})$ .

First, we find for $n = 1$ :

$(1, 0, 0, - \frac{1}{2}), (1, 0, 0, + \frac{1}{2})$

Now, finding for $n = 2$ :

$(2, 0, 0, - \frac{1}{2}), (2, 0, 0, + \frac{1}{2}), (2, 1, - 1, - \frac{1}{2}), (2, 1, - 1, + \frac{1}{2}) (2, 1, 0, - \frac{1}{2}), (2, 1, 0, + \frac{1}{2}), (2, 1, 1, - \frac{1}{2}), (2, 1, 1, + \frac{1}{2})$

Then, finding for $n = 3$ :

$(3, 0, 0, - \frac{1}{2}), (3, 0, 0, + \frac{1}{2}), (3, 1, - 1, - \frac{1}{2}), (3, 1, - 1, + \frac{1}{2}), (3, 1, 0, - \frac{1}{2}), (3, 1, 0, + \frac{1}{2}) (3, 1, 1, - \frac{1}{2}), (3, 1, 1, + \frac{1}{2}), (3, 2, 2, - \frac{1}{2}), (3, 2, 2, + \frac{1}{2}), (3, 2, 1, - \frac{1}{2}), (3, 2, 1, + \frac{1}{2}) (3, 2, 0, - \frac{1}{2}), (3, 2, 0, + \frac{1}{2}), (3, 2, - 1, - \frac{1}{2}), (3, 2, - 1, + \frac{1}{2}), (3, 2, - 2, - \frac{1}{2}), (3, 2, - 2, + \frac{1}{2})$

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!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with $n = 1$ ? With $n = 2$ ? With $n = 3$ ? List the quantum numbers of each state.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Magnetism and Electromagnetic Induction

Particle Model of Matter

Scientific Method Physics

Turning Points in Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom withn=1? Withn=2? Withn=3? List the quantum numbers of each state.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Magnetism and Electromagnetic Induction

Particle Model of Matter

Scientific Method Physics

Turning Points in Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

When all quantum numbers are considered, how many different quantum states are there for a hydrogen atom with $n = 1$ ? With $n = 2$ ? With $n = 3$ ? List the quantum numbers of each state.