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Chemistry | 11th Edition | ISBN: 9780073402680 | Authors: Raymond Chang
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Answer: When an electron makes a transition between energy

Chapter 7, Problem 135P

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QUESTION:

When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum \(\ell\). This is the selection rule, which states that \(\Delta \ell=\pm 1\); that is, in a transition, the value of \(\ell\) can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) \(2s \longrightarrow 1s\), (b) \(3p \longrightarrow 1s\), (c) \(3d \longrightarrow 4f\), (d) \(4d \longrightarrow 3s\)? In view of this selection rule, explain why it is possible to observe the various emission series shown in Figure 7.11.

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QUESTION:

When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum \(\ell\). This is the selection rule, which states that \(\Delta \ell=\pm 1\); that is, in a transition, the value of \(\ell\) can only increase or decrease by one. According to this rule, which of the following transitions are allowed: (a) \(2s \longrightarrow 1s\), (b) \(3p \longrightarrow 1s\), (c) \(3d \longrightarrow 4f\), (d) \(4d \longrightarrow 3s\)? In view of this selection rule, explain why it is possible to observe the various emission series shown in Figure 7.11.

ANSWER:

Step 1  of 2

When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the orbital angular momentum \(\ell\). This is the selection rule, which states that  that is, in a transition, the value of \(\ell\) can only increase or decrease by one.

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