The radius of `5^(@)` Bohr orbit in hydrogen atom is

Options

A. `5r_(0)`
B. `(r_(0)) /( 5)`
C. ` 25r_(0)`
D. `(r_(0))/(25)`

Answer

To find the radius of the 5th Bohr orbit in a hydrogen atom, we can use the formula for the radius of the nth orbit in a hydrogen atom:

\[ r_n = \frac{n^2}{Z} r_0 \]

Where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (which is 5 in this case),
- \( Z \) is the atomic number (which is 1 for hydrogen),
- \( r_0 \) is the radius of the first Bohr orbit (approximately \( 0.529 \) Å).

### Step-by-step Solution:

1. **Identify the values**:
- For hydrogen, \( Z = 1 \).
- The principal quantum number for the 5th orbit is \( n = 5 \).

2. **Substitute the values into the formula**:
\[ r_5 = \frac{n^2}{Z} r_0 = \frac{5^2}{1} r_0 \]

3. **Calculate \( n^2 \)**:
\[ n^2 = 5^2 = 25 \]

4. **Substitute \( n^2 \) back into the equation**:
\[ r_5 = 25 r_0 \]

5. **Conclusion**:
The radius of the 5th Bohr orbit in a hydrogen atom is \( 25 r_0 \).

### Final Answer:
The radius of the 5th Bohr orbit in hydrogen atom is **25 r0**.

---