The radius of the atom (in cm) is of the order of

Options

A. `10^(-10)`
B. `10^(-13)`
C. `10^(-15)`
D. `10^(-8)`

Answer

To determine the radius of an atom in centimeters, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: The radius of an atom is typically measured in angstroms (Å). The radius of a hydrogen atom in its ground state (first orbit) is approximately 0.529 Å.

2. **Identify the Formula**: The formula for the radius of a Bohr atom in the nth orbit is given by:
\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]
where \( n \) is the principal quantum number and \( Z \) is the atomic number. For simplicity, we can consider the ground state (n=1) and Z=1 (for hydrogen).

3. **Convert Angstroms to Centimeters**:
- We know that \( 1 \, \text{Å} = 10^{-10} \, \text{m} \).
- To convert meters to centimeters, we use the conversion factor \( 1 \, \text{m} = 100 \, \text{cm} \).
- Therefore, \( 1 \, \text{Å} = 10^{-10} \, \text{m} \times 100 \, \text{cm/m} = 10^{-10} \times 10^2 \, \text{cm} = 10^{-8} \, \text{cm} \).

4. **Conclusion**: The radius of the atom in centimeters is of the order of \( 10^{-8} \, \text{cm} \).

5. **Select the Correct Option**: Among the given options:
- \( 10^{-10} \)
- \( 10^{-13} \)
- \( 10^{-15} \)
- \( 10^{-8} \)

The correct answer is \( 10^{-8} \, \text{cm} \).

### Final Answer:
The radius of the atom (in cm) is of the order of \( 10^{-8} \).

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