Q. 7 When all quantum numbers are con... [FREE SOLUTION]

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 $n = 1$ :

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

Now, finding for $n = 2$ :

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

Then, finding for $n = 3$ :

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

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91影视

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

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91影视

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

Force

Rotational Dynamics

Wave Optics

Quantum Physics

Solid State Physics

Electromagnetism

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.