The value of four quantum number for the last electron of atom of element 'X' are n=7, l=1,m=+1 and s=+1/2 or -1/2 and vlaue of spin magnetic momentum for element 'X' is zero element 'X' has two isotopes (I) `""_(Z)^(A)X and ` (II) `""_(Z)^(B)X`.
Q. The possible value of all four quantum numbers for 90th electron of atom of element 'X' is:

Options

A. `{:(n,l,m,s),(6,2,0,-1//2):}`
B. `{:(n,l,m,s),(5,2,-1,+1//2):}`
C. `{:(n,l,m,s),(6,0,0,+1//2):}`
D. `{:(n,l,m,s),(5,3,-2,-1//2):}`

Explanation

To find the possible values of all four quantum numbers for the 90th electron of element 'X', we will follow these steps:

### Step 1: Understand the given quantum numbers for the last electron
The last electron of element 'X' has the following quantum numbers:
- Principal quantum number (n) = 7
- Azimuthal quantum number (l) = 1 (indicating a p orbital)
- Magnetic quantum number (m) = +1
- Spin quantum number (s) = +1/2 or -1/2

### Step 2: Determine the total number of electrons
Since the last electron is in the 7p orbital, we need to find the total number of electrons filled before the 90th electron. We will fill the orbitals according to the Aufbau principle.

1. **1s**: 2 electrons
2. **2s**: 2 electrons
3. **2p**: 6 electrons
4. **3s**: 2 electrons
5. **3p**: 6 electrons
6. **4s**: 2 electrons
7. **3d**: 10 electrons
8. **4p**: 6 electrons
9. **5s**: 2 electrons
10. **4d**: 10 electrons
11. **5p**: 6 electrons
12. **6s**: 2 electrons
13. **4f**: 14 electrons
14. **5d**: 10 electrons
15. **6p**: 6 electrons
16. **7s**: 2 electrons
17. **6d**: 10 electrons
18. **7p**: 2 electrons (last electron)

Adding these gives us:
- Total = 2 + 2 + 6 + 2 + 6 + 2 + 10 + 6 + 2 + 10 + 6 + 2 + 14 + 10 + 6 + 2 + 10 + 2 = 88 electrons

### Step 3: Determine the 90th electron
Since we have 88 electrons filled, the 89th and 90th electrons will go into the **5f** orbital, as it is the next available orbital after filling the 7s and before filling the 6d.

### Step 4: Assign quantum numbers for the 90th electron
The quantum numbers for the 90th electron in the 5f orbital are:
- Principal quantum number (n) = 5
- Azimuthal quantum number (l) = 3 (for f orbital)
- Magnetic quantum number (m) can take values from -3 to +3 (i.e., -3, -2, -1, 0, +1, +2, +3)
- Spin quantum number (s) can be either +1/2 or -1/2

### Conclusion
The possible values of all four quantum numbers for the 90th electron of element 'X' are:
- n = 5
- l = 3
- m = -3, -2, -1, 0, +1, +2, +3
- s = +1/2 or -1/2