8. According to the quantum theory, how many (d) orbitals are d. 7 a. 1 b. 3 8.911 c. 5 e. d orbitals are not allowed in the n = 4 shell

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### Quantum Theory and Orbital Question

#### Multiple-Choice Question:
According to the quantum theory, how many \( (d) \) orbitals are there in the \( n = 4 \) shell?

**Options:**
- a. 1
- b. 3
- c. 5
- d. 7
- e. d orbitals are not allowed in the \( n = 4 \) shell.

#### Detailed Explanation:
In the context of quantum theory, the principal quantum number \( n \) can have any positive integer value. The \( n = 4 \) shell can have \( s \), \( p \), \( d \), and \( f \) orbitals:
- **1** \( s \) orbital 
- **3** \( p \) orbitals 
- **5** \( d \) orbitals 
- **7** \( f \) orbitals 

Therefore, the correct answer to this question is **c. 5**.

This exercise is part of learning the distribution of electrons in atomic orbitals according to quantum mechanical principles.
Transcribed Image Text:### Quantum Theory and Orbital Question #### Multiple-Choice Question: According to the quantum theory, how many \( (d) \) orbitals are there in the \( n = 4 \) shell? **Options:** - a. 1 - b. 3 - c. 5 - d. 7 - e. d orbitals are not allowed in the \( n = 4 \) shell. #### Detailed Explanation: In the context of quantum theory, the principal quantum number \( n \) can have any positive integer value. The \( n = 4 \) shell can have \( s \), \( p \), \( d \), and \( f \) orbitals: - **1** \( s \) orbital - **3** \( p \) orbitals - **5** \( d \) orbitals - **7** \( f \) orbitals Therefore, the correct answer to this question is **c. 5**. This exercise is part of learning the distribution of electrons in atomic orbitals according to quantum mechanical principles.
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