Book edition 2nd Edition

Author(s) Randy Harris

Pages 633 pages

ISBN 9780805303087

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Short Answer

In its ground state, carbon's 2p electrons interact to produce $j_{T} = 0$ . Given Hund's rule. what does this say about the total orbital angular momentum of these electrons?

Total orbital angular momentum is $L = \sqrt{2} h$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Total spin of two electrons

The total spin of the two electrons $S_{T}$ is

$S_{T} = \sqrt{S_{T} (S_{T} + 1)} h$ ….(1)

Step 2: total spin quantum number

The quantum number j_T is zero $j_{T} = 0$ .

The spin quantum number of each electron is $s_{1} = s_{2} = \frac{1}{2}$ .

By using Hund's rule, we conclude that the total spin quantum number s_t is given by

$\begin{array}{rcl} S_{T} & = & s_{1} + s_{2} \\ = & \frac{1}{2} + \frac{1}{2} \\ S_{T} & = & 1 \end{array}$

Step 3: total spin of electrons

By using Eq. (I), we find the total spin of the electrons s_T as

$\begin{array}{rcl} S_{T} & = & \sqrt{s_{T} (s_{T} + 1)} h \\ = & \sqrt{1 . (1 + 1)} h \\ S_{T} & = & \sqrt{2} h \end{array}$

Step 4: The total orbital angular momentum LT

Now, since $j_{T} = 0$ , we conclude that the total orbital angular momentum L_T must be equal to the total spin S_T

$L_{T} = S_{T} = \sqrt{2} h$

Hence the total orbital angular momentum is $L_{T} = \sqrt{2} h$ .

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Modern Physics

Answers without the blur.

Short Answer

In its ground state, carbon's 2p electrons interact to produce $j_{T} = 0$ . Given Hund's rule. what does this say about the total orbital angular momentum of these electrons?

Step by Step Solution

Step 1: Total spin of two electrons

Step 2: total spin quantum number

Step 3: total spin of electrons

Step 4: The total orbital angular momentum LT

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Modern Physics

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Short Answer

In its ground state, carbon's 2p electrons interact to produce jT=0. Given Hund's rule. what does this say about the total orbital angular momentum of these electrons?

Step by Step Solution

Step 1: Total spin of two electrons

Step 2: total spin quantum number

Step 3: total spin of electrons

Step 4: The total orbital angular momentum LT

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