The ratio of difference in the number of electrons between K and M shells is `3 : 2` for X and Y elements respectively . 'X' possesses stable electronic configuration and M is the valence shell for both X and Y. Give the electronic configurations of X and y.

Options

A. 2 , 8 , 5 and 2 , 8 , 4
B. 2 , 8 , 8 and 2 , 8 , 6
C. 2 , 8 , 8 and 2 , 6 , 6
D. 2 , 8 , 6 and 2 , 8 , 4

Explanation

To solve the problem, we need to determine the electronic configurations of elements X and Y based on the given information about the ratio of the difference in the number of electrons between the K and M shells.

### Step 1: Understand the Shells
The K shell can hold a maximum of 2 electrons, and the M shell can hold a maximum of 8 electrons. The difference in the number of electrons between the K and M shells can be expressed as:
\[ \text{Difference} = K - M \]

### Step 2: Set Up the Ratios
According to the problem, the ratio of the difference in the number of electrons between the K and M shells for elements X and Y is given as:
\[ \frac{K - M \text{ (for X)}}{K - M \text{ (for Y)}} = \frac{3}{2} \]

Let’s denote:
- \( K_X \) and \( M_X \) as the number of electrons in K and M shells for element X.
- \( K_Y \) and \( M_Y \) as the number of electrons in K and M shells for element Y.

From the ratio, we can write:
\[ \frac{K_X - M_X}{K_Y - M_Y} = \frac{3}{2} \]

### Step 3: Assign Values
Since K can hold a maximum of 2 electrons, we can set:
- For element X, let \( K_X = 2 \) (maximum for K shell).
- For element Y, let \( K_Y = 2 \) (maximum for K shell).

Now, we can express the differences:
- For element X: \( K_X - M_X = 2 - M_X \)
- For element Y: \( K_Y - M_Y = 2 - M_Y \)

### Step 4: Substitute into the Ratio
Substituting into the ratio gives:
\[ \frac{2 - M_X}{2 - M_Y} = \frac{3}{2} \]

### Step 5: Cross-Multiply
Cross-multiplying gives:
\[ 2(2 - M_X) = 3(2 - M_Y) \]
Expanding both sides:
\[ 4 - 2M_X = 6 - 3M_Y \]

### Step 6: Rearranging the Equation
Rearranging the equation gives:
\[ 3M_Y - 2M_X = 2 \]

### Step 7: Determine Possible Values
Since M can hold a maximum of 8 electrons, we can try different values for \( M_X \) and \( M_Y \) that satisfy the equation.

Assuming \( M_X = 8 \) (which is not stable), we can check:
- If \( M_X = 6 \), then \( 3M_Y - 2(6) = 2 \) gives \( 3M_Y = 14 \) or \( M_Y = \frac{14}{3} \) (not an integer).
- If \( M_X = 5 \), then \( 3M_Y - 10 = 2 \) gives \( 3M_Y = 12 \) or \( M_Y = 4 \) (valid).

### Step 8: Final Configurations
Thus, we have:
- For element X: \( K_X = 2, M_X = 5 \) → Electronic configuration: \( 2, 5 \)
- For element Y: \( K_Y = 2, M_Y = 4 \) → Electronic configuration: \( 2, 4 \)

### Conclusion
The electronic configurations are:
- Element X: \( 2, 5 \) (total 7 electrons)
- Element Y: \( 2, 4 \) (total 6 electrons)