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 value 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 value of A and B respectively are:

Options

A. 118 and 136
B. 218 and 236
C. 236 and 254
D. 226 and 244

Explanation

To solve the problem, we need to determine the values of A and B for the isotopes of element X based on the provided quantum numbers and the information about its magnetic moment.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The quantum numbers given are:
- Principal quantum number (n) = 7
- Azimuthal quantum number (l) = 1
- Magnetic quantum number (m) = +1
- Spin quantum number (s) = +1/2 or -1/2
- Since l = 1, the orbital is a p-orbital. Therefore, we are dealing with the 7p orbital.

2. **Determine the Element**:
- The last electron is in the 7p orbital. The element with the atomic number (Z) that ends in the 7p orbital is Radon (Rn), which has an atomic number of 86.
- The complete electron configuration for Radon is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s² 7p⁶

3. **Magnetic Moment**:
- The problem states that the spin magnetic moment of element X is zero. This indicates that there are no unpaired electrons in the outermost shell, meaning the 7p orbital is completely filled.

4. **Determine the Atomic Number**:
- Since the last electron is in the 7p orbital and it is completely filled, the atomic number (Z) of element X is 118.

5. **Find the Mass Numbers A and B**:
- The mass number (A) is the sum of protons and neutrons. For isotopes of element X (which has Z = 118), we can express the mass number as:
- A = Z + N (where N is the number of neutrons)
- We know that the difference between the two isotopes is 18:
- B - A = 18
- Let’s express B in terms of A:
- B = A + 18

6. **Calculate A and B**:
- We can set up the equations:
- A = 118 + N (for isotope I)
- B = A + 18 = (118 + N) + 18 = 136 + N (for isotope II)
- Since both isotopes must have the same number of protons (Z = 118), we can express the mass numbers:
- A = 118 + N
- B = 136 + N
- The difference between B and A is:
- (136 + N) - (118 + N) = 18, which is consistent.

7. **Final Values**:
- If we assume the most common case where the number of neutrons is equal to the number of protons (N ≈ Z), we can find:
- For A, if N = 118, then A = 118 + 118 = 236.
- For B, if N = 118, then B = 136 + 118 = 254.

Thus, the values of A and B are:
- A = 236
- B = 254

### Final Answer:
The values of A and B respectively are 236 and 254.