Number of times radius of the 3rd shell of the H-atom as compared to that of radius of first shell is

Explanation

To find the number of times the radius of the 3rd shell of the hydrogen atom is compared to that of the radius of the 1st shell, we can use the formula for the radius of an electron shell in a hydrogen atom.

### Step-by-Step Solution:

1. **Understand the Formula for Radius**:
The radius of the nth shell of a hydrogen atom is given by the formula:
\[ r_n = a_0 \cdot \frac{n^2}{Z} \]
where:
- \( r_n \) is the radius of the nth shell,
- \( a_0 \) is the Bohr radius (approximately \( 0.529 \, \text{Å} \)),
- \( n \) is the principal quantum number (1 for the first shell, 2 for the second shell, etc.),
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)).

2. **Calculate the Radius of the 1st Shell**:
For the 1st shell (\( n = 1 \)):
\[ r_1 = a_0 \cdot \frac{1^2}{1} = a_0 \]

3. **Calculate the Radius of the 3rd Shell**:
For the 3rd shell (\( n = 3 \)):
\[ r_3 = a_0 \cdot \frac{3^2}{1} = a_0 \cdot 9 = 9a_0 \]

4. **Compare the Radii**:
Now, we need to find how many times the radius of the 3rd shell is compared to the radius of the 1st shell:
\[ \text{Ratio} = \frac{r_3}{r_1} = \frac{9a_0}{a_0} = 9 \]

5. **Conclusion**:
Therefore, the radius of the 3rd shell is 9 times the radius of the 1st shell.

### Final Answer:
The radius of the 3rd shell of the hydrogen atom is 9 times that of the radius of the 1st shell.