How many subshells and electrons are associated with n = 4?

Options

A. 32, 64
B. 16, 32
C. 4, 16
D. 8, 16

Explanation

To determine the number of subshells and electrons associated with n = 4, we can follow these steps:

### Step 1: Identify the principal quantum number (n)
The principal quantum number (n) indicates the energy level of the electron. In this case, n = 4.

**Hint:** The principal quantum number (n) can take positive integer values (1, 2, 3, ...).

### Step 2: Determine the number of subshells
For any principal quantum number n, the number of subshells is equal to n. Therefore, for n = 4, there are 4 subshells.

**Hint:** The subshells are designated as s, p, d, and f. For n = 4, they are 4s, 4p, 4d, and 4f.

### Step 3: List the subshells
The subshells associated with n = 4 are:
- 4s
- 4p
- 4d
- 4f

**Hint:** Each subshell corresponds to a specific type of orbital.

### Step 4: Determine the number of orbitals in each subshell
- The 4s subshell has 1 orbital.
- The 4p subshell has 3 orbitals.
- The 4d subshell has 5 orbitals.
- The 4f subshell has 7 orbitals.

**Hint:** The number of orbitals in a subshell is given by the formula:
- s subshell: 1 orbital
- p subshell: 3 orbitals
- d subshell: 5 orbitals
- f subshell: 7 orbitals

### Step 5: Calculate the total number of orbitals
Now, we add the number of orbitals from all the subshells:
- Total orbitals = 1 (from 4s) + 3 (from 4p) + 5 (from 4d) + 7 (from 4f) = 16 orbitals.

**Hint:** Make sure to add the number of orbitals from each subshell carefully.

### Step 6: Calculate the total number of electrons
Each orbital can hold a maximum of 2 electrons. Therefore, the total number of electrons is:
- Total electrons = 2 × Total orbitals = 2 × 16 = 32 electrons.

**Hint:** Remember that each orbital can hold 2 electrons, which is a fundamental principle in quantum chemistry.

### Final Answer
- Number of subshells = 4
- Total number of electrons = 32

### Summary of the Solution
For n = 4:
- Number of subshells = 4 (4s, 4p, 4d, 4f)
- Total number of electrons = 32