The set of quantum numbers of the outermost electron for copper in its ground state is.............

Options

A. `4, 1, 1, +(1)/(2)`
B. `3,2,2,+1//2`
C. `4,0,0, +(1)/(2)`
D. `4,2,2,+1//2`

Explanation

To find the set of quantum numbers for the outermost electron of copper in its ground state, we will follow these steps:

### Step 1: Determine the Electron Configuration of Copper
Copper (Cu) has an atomic number of 29. The electron configuration for copper in its ground state is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^{10} \]

### Step 2: Identify the Outermost Electron
From the electron configuration, we can see that the outermost electron is in the \(4s\) subshell. Therefore, the last electron added is in the \(4s^1\) orbital.

### Step 3: Assign the Principal Quantum Number (n)
The principal quantum number \(n\) indicates the energy level of the electron. For the \(4s\) orbital, the value of \(n\) is:
\[ n = 4 \]

### Step 4: Assign the Azimuthal Quantum Number (l)
The azimuthal quantum number \(l\) defines the shape of the orbital. For an \(s\) orbital, \(l\) is:
\[ l = 0 \]

### Step 5: Assign the Magnetic Quantum Number (m)
The magnetic quantum number \(m\) can take values from \(-l\) to \(+l\). Since \(l = 0\), the only possible value for \(m\) is:
\[ m = 0 \]

### Step 6: Assign the Spin Quantum Number (s)
The spin quantum number \(s\) can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\). For the outermost electron in copper, we will take:
\[ s = +\frac{1}{2} \]

### Final Answer
Thus, the set of quantum numbers for the outermost electron of copper in its ground state is:
\[ (n, l, m, s) = (4, 0, 0, +\frac{1}{2}) \]