The energy, radius and velocity of the electron in the hydrogen atom in the ground state are `-13.6 eV, 0.53 Å` and `2.188 xx 10^(8) m s^(-1)` respectively.
The radius of the third orbit of hydrogen atom will be

Options

A. `1.59 Å`
B. `4.77 Å`
C. `3.0 Å`
D. `6.0 Å`

Explanation

To find the radius of the third orbit of a hydrogen atom, we can use the formula for the radius of the nth orbit in a hydrogen atom:

\[ R_n = R_0 \cdot n^2 \]

where:
- \( R_n \) is the radius of the nth orbit,
- \( R_0 \) is the radius of the ground state (first orbit),
- \( n \) is the principal quantum number (orbit number).

### Step-by-step Solution:

1. **Identify the given values:**
- The radius of the ground state (first orbit), \( R_0 = 0.53 \) Å.
- The principal quantum number for the third orbit, \( n = 3 \).

2. **Substitute the values into the formula:**
\[ R_3 = R_0 \cdot n^2 \]
\[ R_3 = 0.53 \, \text{Å} \cdot (3^2) \]

3. **Calculate \( n^2 \):**
\[ n^2 = 3^2 = 9 \]

4. **Multiply to find \( R_3 \):**
\[ R_3 = 0.53 \, \text{Å} \cdot 9 \]
\[ R_3 = 4.77 \, \text{Å} \]

5. **Final result:**
The radius of the third orbit of the hydrogen atom is \( 4.77 \) Å.