To determine the possible quantum numbers for the last electron of gallium (Ga), we will follow these steps:
### Step 1: Identify the Electron Configuration of Gallium
Gallium (Ga) has an atomic number of 31. Its electron configuration is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p¹
### Step 2: Determine the Last Electron
The last electron in gallium is added to the 4p subshell. Therefore, the last electron is in the 4p orbital.
### Step 3: Identify the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For the last electron in gallium, which is in the 4p orbital, n = 4.
### Step 4: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For p orbitals, l = 1. Therefore, for the last electron in the 4p orbital, l = 1.
### Step 5: Identify the Magnetic Quantum Number (m_l)
The magnetic quantum number (m_l) can take values from -l to +l. For l = 1, m_l can be -1, 0, or +1. Therefore, the possible values for m_l are -1, 0, and +1.
### Step 6: Identify the Spin Quantum Number (m_s)
The spin quantum number (m_s) can take values of +1/2 or -1/2. For the last electron, we can choose either value.
### Step 7: Combine the Quantum Numbers
Based on the above information, the possible sets of quantum numbers for the last electron of gallium can be:
1. (n = 4, l = 1, m_l = -1, m_s = +1/2)
2. (n = 4, l = 1, m_l = 0, m_s = +1/2)
3. (n = 4, l = 1, m_l = +1, m_s = +1/2)
4. (n = 4, l = 1, m_l = -1, m_s = -1/2)
5. (n = 4, l = 1, m_l = 0, m_s = -1/2)
6. (n = 4, l = 1, m_l = +1, m_s = -1/2)
### Conclusion
The possible quantum numbers for the last electron of gallium can be represented as:
- (4, 1, m_l, m_s) where m_l can be -1, 0, +1 and m_s can be +1/2 or -1/2.
