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Found in: Page 1247

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

How many electron states are there in the following shells: (a) n = 4 , (b) n = 1 , (c) n = 3 , (d) n = 2 ?

1. There are 32 electron states in shell of n =4.
2. There are 2 electron states in shell of n = 1 .
3. There are 18 electron states in shell of n = 3 .
4. There are 8 electron states in shell of n = 2 .
See the step by step solution

Step 1: The given data:

The given quantum numbers are:

1. n = 4
2. n = 1
3. n = 3
4. n = 2

Step 2: Understanding the concept of electron states:

The electronic state is defined by the configuration of the electron system, as well as the quantum numbers of each electron that contributes to that configuration.

Using the concept of electron states for each given quantum number, define the required number of electron states by substituting the given value in the below formula.

The number of electron states presents in the shell for each given value of n ,

$N=2{n}^{2}$ ….. (1)

Step 3: (a) Calculation of electron states for  n = 4

Using the given value of quantum number n = 4 in equation (1), the number of electron states can be given as follows:

$\begin{array}{l}N=2\left(4{\right)}^{2}\\ =32\end{array}$

Hence, there are 32 electron states in the shell.

Step 4: (b) Calculation of electron states for  n = 1:

Using the given value n = 1 in equation (1), the number of electron states can be given as follows:

$N=2{\left(1\right)}^{2}\phantom{\rule{0ex}{0ex}}=2$

Hence, there are 2 electron states in the shell.

Step 5: (c) Calculation of electron states for n = 3 :

Using the given value n = 3 in equation (1), the number of electron states can be given as follows:

$N=2{\left(3\right)}^{2}\phantom{\rule{0ex}{0ex}}=18$

Hence, there are 18 electron states in the shell.

Step 6: (d) Calculation of electron states for n = 2 :

Using the given value n = 2 in equation (1), the number of electron states can be given as follows:

$N=2{\left(2\right)}^{2}\phantom{\rule{0ex}{0ex}}=8$

Hence, there are 8 electron states in the shell.