The characteristic X-rays for the lines of `K_(a)` series in element X and Y are `9.87 Å and 14.6 Å` respectively .If Moseley's equation `sqrt(v) = 4.9 xx 10^(7) (Z - 0.75)` is followed:
The atomic number of Y is

Options

A. 10
B. 6
C. 8
D. 12

Explanation

To find the atomic number of element Y using the given information and Moseley's equation, we will follow these steps:

### Step 1: Convert the wavelength of Y to frequency
The wavelength of the characteristic X-ray for element Y is given as 14.6 Å. We need to convert this to meters and then use the speed of light to find the frequency.

1. Convert 14.6 Å to meters:
\[ 14.6 \, \text{Å} = 14.6 \times 10^{-10} \, \text{m} \]

2. Use the formula for frequency:
\[ v = \frac{c}{\lambda} \]
where \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light) and \( \lambda = 14.6 \times 10^{-10} \, \text{m} \).

3. Substitute the values:
\[ v = \frac{3 \times 10^8}{14.6 \times 10^{-10}} \approx 2.05 \times 10^{18} \, \text{Hz} \]

### Step 2: Apply Moseley's equation
Moseley's equation is given as:
\[ \sqrt{v} = 4.9 \times 10^7 (Z - 0.75) \]

1. Calculate \(\sqrt{v}\):
\[ \sqrt{v} = \sqrt{2.05 \times 10^{18}} \approx 4.53 \times 10^9 \]

2. Substitute \(\sqrt{v}\) into Moseley's equation:
\[ 4.53 \times 10^9 = 4.9 \times 10^7 (Z - 0.75) \]

### Step 3: Solve for Z
1. Rearranging the equation to solve for Z:
\[ Z - 0.75 = \frac{4.53 \times 10^9}{4.9 \times 10^7} \]

2. Calculate the right-hand side:
\[ Z - 0.75 \approx 92.43 \]

3. Add 0.75 to both sides:
\[ Z \approx 92.43 + 0.75 \approx 93.18 \]

4. Since Z must be a whole number, we round it to the nearest whole number:
\[ Z \approx 93 \]

### Conclusion
The atomic number of element Y is approximately **93**.

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