The dimension of the Rydberg constant are

Options

A. `M^(@)L^(-1)T`
B. `MLT^(-1)`
C. `M^(@)L^(-1)T^(@)`
D. `ML^(@)T^(2)`

Explanation

To find the dimension of the Rydberg constant (R), we start by understanding its relationship with the wavelength (λ) in the context of the Rydberg formula. The Rydberg formula is given by:

\[ \frac{1}{\lambda} = R z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Where:
- \( \lambda \) is the wavelength,
- \( R \) is the Rydberg constant,
- \( z \) is the atomic number,
- \( n_1 \) and \( n_2 \) are principal quantum numbers.

### Step 1: Identify the dimensions of \( \lambda \)
The wavelength \( \lambda \) has dimensions of length. In SI units, it is measured in meters (m). Therefore, the dimension of wavelength is:

\[ [\lambda] = L \]

### Step 2: Determine the dimensions of \( \frac{1}{\lambda} \)
Since \( \frac{1}{\lambda} \) is the reciprocal of the wavelength, its dimension can be expressed as:

\[ \left[\frac{1}{\lambda}\right] = \frac{1}{[L]} = L^{-1} \]

### Step 3: Relate the dimensions of \( R \) to \( \frac{1}{\lambda} \)
From the Rydberg formula, we see that \( R \) is multiplied by a dimensionless quantity \( z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \). Since this entire term is dimensionless, the dimensions of \( R \) must be the same as the dimensions of \( \frac{1}{\lambda} \):

\[ [R] = \left[\frac{1}{\lambda}\right] = L^{-1} \]

### Conclusion
Thus, the dimension of the Rydberg constant \( R \) is:

\[ [R] = L^{-1} \]