Total number of elements which are present in a row on the periodic table between those elements, whose wavelength of `K_(alpha)` lines are equal to 250 and 179 pm are ( Rydberg constant = `1.097xx10^7m^-1` )

Answer

To solve the problem, we need to find the total number of elements present in a row on the periodic table between the elements whose K_alpha wavelengths are equal to 250 pm and 179 pm. We will use Moseley's law to relate the wavelengths to the atomic numbers.

### Step-by-step Solution:

1. **Understanding Moseley's Law**:
Moseley's law states that the square root of the frequency (f) of the emitted X-rays is proportional to the atomic number (Z) of the element:
\[ f = a(Z - b) \]
where \( a \) and \( b \) are constants.

2. **Relating Wavelength to Frequency**:
The frequency \( f \) is related to the wavelength \( \lambda \) by the equation:
\[ f = \frac{1}{\lambda} \]
Therefore, we can rewrite Moseley's law in terms of wavelength:
\[ \frac{1}{\lambda} = a(Z - b) \]

3. **Using the Rydberg Constant**:
Given that the Rydberg constant \( a = 1.097 \times 10^7 \, \text{m}^{-1} \), we can substitute this value into our equation.

4. **Calculating for \( \lambda = 250 \, \text{pm} \)**:
Convert \( \lambda \) into meters:
\[ \lambda = 250 \, \text{pm} = 250 \times 10^{-12} \, \text{m} \]
Now, substitute into the equation:
\[ \frac{1}{250 \times 10^{-12}} = 1.097 \times 10^7 (Z - 1) \]
Solving for \( Z \):
\[ 4 \times 10^{6} = 1.097 \times 10^7 (Z - 1) \]
\[ Z - 1 = \frac{4 \times 10^{6}}{1.097 \times 10^7} \]
\[ Z - 1 \approx 0.364 \implies Z \approx 23 \]

5. **Calculating for \( \lambda = 179 \, \text{pm} \)**:
Convert \( \lambda \) into meters:
\[ \lambda = 179 \, \text{pm} = 179 \times 10^{-12} \, \text{m} \]
Substitute into the equation:
\[ \frac{1}{179 \times 10^{-12}} = 1.097 \times 10^7 (Z - 1) \]
Solving for \( Z \):
\[ 5.58 \times 10^{6} = 1.097 \times 10^7 (Z - 1) \]
\[ Z - 1 = \frac{5.58 \times 10^{6}}{1.097 \times 10^7} \]
\[ Z - 1 \approx 0.508 \implies Z \approx 27 \]

6. **Finding the Total Number of Elements**:
The atomic numbers corresponding to the wavelengths are \( Z = 23 \) and \( Z = 27 \). The elements between these atomic numbers are:
- 24 (Chromium)
- 25 (Manganese)
- 26 (Iron)

Therefore, the total number of elements between atomic numbers 23 and 27 is:
\[ 27 - 23 - 1 = 3 \]

### Final Answer:
The total number of elements present in a row on the periodic table between those elements is **3**.