To solve the question regarding the ground state of \( \text{Cu}^+ \), we will follow these steps:
### Step 1: Determine the Atomic Number and Electron Configuration of Copper
Copper (Cu) has an atomic number of 29. The electron configuration for neutral copper is:
\[
\text{Cu}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^{10} \, 4s^1
\]
### Step 2: Adjust the Electron Configuration for \( \text{Cu}^+ \)
To find the electron configuration of \( \text{Cu}^+ \), we remove one electron from the neutral copper atom. The electron is removed from the outermost shell, which is the 4s subshell:
\[
\text{Cu}^+: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^{10}
\]
### Step 3: Count the Number of Shells Occupied
The shells are defined by the principal quantum number \( n \):
- \( n = 1 \): 1s
- \( n = 2 \): 2s, 2p
- \( n = 3 \): 3s, 3p, 3d
From the configuration of \( \text{Cu}^+ \), the occupied shells are:
- Shell 1 (1s)
- Shell 2 (2s, 2p)
- Shell 3 (3s, 3p, 3d)
Thus, the number of shells occupied is **3**.
### Step 4: Count the Number of Subshells Occupied
The subshells occupied in \( \text{Cu}^+ \) are:
- 1s
- 2s
- 2p
- 3s
- 3p
- 3d
This gives us a total of **6 subshells** occupied.
### Step 5: Count the Number of Filled Orbitals
The filled orbitals in \( \text{Cu}^+ \) are:
- 1s (1 orbital)
- 2s (1 orbital)
- 2p (3 orbitals: 2px, 2py, 2pz)
- 3s (1 orbital)
- 3p (3 orbitals: 3px, 3py, 3pz)
- 3d (5 orbitals: 3dxy, 3dyz, 3dzx, 3dx²-y², 3dz²)
Counting these gives:
\[
1 + 1 + 3 + 1 + 3 + 5 = 14 \text{ filled orbitals}
\]
### Step 6: Count the Number of Unpaired Electrons
In the electron configuration of \( \text{Cu}^+ \), all electrons are paired:
- 1s² (2 electrons, paired)
- 2s² (2 electrons, paired)
- 2p⁶ (6 electrons, paired)
- 3s² (2 electrons, paired)
- 3p⁶ (6 electrons, paired)
- 3d¹⁰ (10 electrons, paired)
Thus, the number of unpaired electrons is **0**.
### Final Answer
The number of shells occupied, subshells occupied, filled orbitals, and unpaired electrons in \( \text{Cu}^+ \) are:
- **3, 6, 14, 0**
