Two elements X and Y have 6 and 7 electrons in their N- and M-shells, respectively. Find the ratio of atomic numbers of X and Y.

Options

A. `3:4`
B. `1:2`
C. `2:1`
D. `6:7`

Answer

To find the ratio of atomic numbers of elements X and Y based on the given information about their electron configurations, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Electron Configuration**:
- Element X has 6 electrons in its N-shell.
- Element Y has 7 electrons in its M-shell.

2. **Determine the Shell Capacities**:
- The maximum number of electrons that can be held in each shell is as follows:
- K-shell: 2 electrons
- L-shell: 8 electrons
- M-shell: 18 electrons
- N-shell: 32 electrons

3. **Calculate the Total Electrons for Element X**:
- Since X has 6 electrons in the N-shell, we can fill the previous shells:
- K-shell: 2 electrons
- L-shell: 8 electrons
- N-shell: 6 electrons
- Total electrons for X = K + L + N = 2 + 8 + 6 = 16 electrons.

4. **Calculate the Total Electrons for Element Y**:
- Since Y has 7 electrons in the M-shell, we can fill the previous shells:
- K-shell: 2 electrons
- L-shell: 8 electrons
- M-shell: 7 electrons
- Total electrons for Y = K + L + M = 2 + 8 + 7 = 17 electrons.

5. **Determine Atomic Numbers**:
- The atomic number of an element is equal to the total number of electrons in a neutral atom.
- Therefore, the atomic number of X = 16 and the atomic number of Y = 17.

6. **Calculate the Ratio of Atomic Numbers**:
- The ratio of atomic numbers of X to Y is:
\[ \text{Ratio} = \frac{\text{Atomic Number of X}}{\text{Atomic Number of Y}} = \frac{16}{17} \]

### Final Answer:
The ratio of atomic numbers of X and Y is \( \frac{16}{17} \).