Atoms `._(7)X^(A),._(8)Y^(B)` and `._(9)Z^(17)` are such that `._(8)Y` is an isobar of `._(7)X` and atom `._(9)Z^(17)` is isotone of `._(8)Y`. Mass no. of `X` and no of neutrons in `Y` are respectively `:`

Options

A. 8,8
B. 17,7
C. 9,8
D. 16,8

Answer

To solve the problem, we need to analyze the relationships between the atoms \( _{7}X^{A} \), \( _{8}Y^{B} \), and \( _{9}Z^{17} \) based on the definitions of isobars and isotones.

### Step-by-Step Solution:

1. **Identify Isobars**:
- Isobars are atoms that have the same mass number but different atomic numbers.
- Given that \( _{8}Y \) is an isobar of \( _{7}X \), we can conclude that the mass number \( A \) of \( _{7}X \) is equal to the mass number \( B \) of \( _{8}Y \).
- Therefore, we have:
\[ A = B \]

2. **Identify Isotones**:
- Isotones are atoms that have the same number of neutrons but different atomic numbers.
- Given that \( _{9}Z^{17} \) is an isotone of \( _{8}Y \), we need to find the number of neutrons in both \( _{9}Z^{17} \) and \( _{8}Y \).

3. **Calculate Neutrons in \( _{9}Z^{17} \)**:
- The mass number of \( _{9}Z^{17} \) is 17, and its atomic number is 9.
- The number of neutrons \( N \) can be calculated using the formula:
\[ N = \text{Mass number} - \text{Atomic number} \]
- Thus, for \( _{9}Z^{17} \):
\[ N = 17 - 9 = 8 \]

4. **Set Up Equation for Neutrons in \( _{8}Y \)**:
- Since \( _{9}Z^{17} \) is an isotone of \( _{8}Y \), the number of neutrons in \( _{8}Y \) must also be 8.
- The number of neutrons in \( _{8}Y \) can be expressed as:
\[ \text{Number of neutrons in } Y = B - \text{Atomic number of } Y \]
- The atomic number of \( _{8}Y \) is 8, so:
\[ \text{Number of neutrons in } Y = B - 8 \]

5. **Equate Neutrons**:
- Since the number of neutrons in \( _{9}Z^{17} \) is equal to the number of neutrons in \( _{8}Y \):
\[ 8 = B - 8 \]
- Solving for \( B \):
\[ B = 8 + 8 = 16 \]

6. **Determine Mass Number \( A \)**:
- From the relationship established earlier, since \( A = B \):
\[ A = 16 \]

### Final Answers:
- The mass number of \( X \) (i.e., \( A \)) is 16.
- The number of neutrons in \( Y \) (i.e., \( B - 8 \)) is 8.

### Summary:
The mass number of \( X \) is 16 and the number of neutrons in \( Y \) is 8.