Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

An electron in a multi-electron atom has $m_{l} = + 4$ For this electron, what are (a) the value of I, (b) the smallest possible value of n, and (c) the number of possible values of $m_{s}$ ?

The value of is 4 .
The smallest possible value of n is 5.
The number of possible values of $m_{s}$ is 2.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data:

An electron in a multi-electron atom has $m_{1} = + 4$ .

Step 2: Understanding the concept of quantum number of an electron:

For every value of the orbital quantum number, there exist (21+1) values of magnetic quantum number ranging from -I to +I. Thus, the maximum value of this magnetic quantum number is equal to the value of the orbital quantum number. Now, for every value of the principal quantum number, there are n values of I ranging from 0 to (n-1) . Thus, the smallest value of n is given by (I+1). Now, every electron has two spin orientations, thus the value of the magnetic quantum number is determined by these spins.

Formula:

The smallest possible value of n is

n =I +1 ….. (1)

Step 3: (a) Calculation of the value of :

The value of $l$ considering the table is given by,

$I = {(m_{I})}_{\max} = 4$

Hence, the value is 4.

Step 4: b) Calculation of the smallest possible value of :

Using the above value of I=4 in equation (1), we can get the smallest possible value of n as follows:

n = 4 + 1

Hence, the smallest possible value of is 5.

Step 5: c) Calculation of the number of possible values of ms :

Using the concept, we know that there are two possible spin orientations of electron,

$m_{s} = \pm \frac{1}{2}$

Hence, there are two possible values.

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Fundamentals Of Physics

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Short Answer

An electron in a multi-electron atom has $m_{l} = + 4$ For this electron, what are (a) the value of I, (b) the smallest possible value of n, and (c) the number of possible values of $m_{s}$ ?

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of quantum number of an electron:

Step 3: (a) Calculation of the value of :

Step 4: b) Calculation of the smallest possible value of :

Step 5: c) Calculation of the number of possible values of ms :

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Fundamentals Of Physics

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Short Answer

An electron in a multi-electron atom has ml=+4 For this electron, what are (a) the value of I, (b) the smallest possible value of n, and (c) the number of possible values of ms?

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of quantum number of an electron:

Step 3: (a) Calculation of the value of :

Step 4: b) Calculation of the smallest possible value of :

Step 5: c) Calculation of the number of possible values of ms :

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An electron in a multi-electron atom has $m_{l} = + 4$ For this electron, what are (a) the value of I, (b) the smallest possible value of n, and (c) the number of possible values of $m_{s}$ ?