The radius of the stationary state which is also called Bohr radius is given by the expression `r_(n)=n^(2)a_(0)` where the value of `a_(0)` is

Options

A. 52.9 pm
B. 5.29 pm
C. 529 pm
D. 0.529 pm

Explanation

To find the value of the Bohr radius \( a_0 \) in the context of the stationary states of hydrogen and hydrogen-like atoms, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Expression**: The radius of the stationary state is given by the formula:
\[ r_n = n^2 a_0 \]
where \( r_n \) is the radius of the nth orbit, \( n \) is the principal quantum number, and \( a_0 \) is the Bohr radius.

2. **Identify the Value of \( a_0 \)**: The problem specifically asks for the value of \( a_0 \). From the theory of atomic structure, particularly in the Bohr model, the value of \( a_0 \) is known to be:
\[ a_0 = 52.9 \text{ picometers} \]

3. **Contextualize the Value**: The Bohr radius represents the radius of the first orbit (when \( n = 1 \)) of the hydrogen atom. This means that for hydrogen, when the electron is in its lowest energy state, it is approximately 52.9 picometers away from the nucleus.

4. **Conclusion**: Therefore, the value of \( a_0 \) is:
\[ \boxed{52.9 \text{ picometers}} \]