Question

The polarizability of atoms in the air molecule is \( 9.7 \times 10^{-41} \, \text{cm}^2/\text{V} \). The radius of the atom of an air molecule is:

• A. \( 9.6 \times 10^{-11} \, \text{m} \)
• B. \( 9.6 \times 10^{-12} \, \text{m} \)
• C. \( 9.6 \times 10^{-13} \, \text{m} \)
• D. \( 9.6 \times 10^{-14} \, \text{m} \)

Answer 1

The Correct Option is A

We can calculate the radius of the atom by using the formula for polarizability:

\[ \alpha = \frac{4 \pi \epsilon_0 r^3}{3} \]

Given \( \alpha = 9.7 \times 10^{-41} \, \text{cm}^2/\text{V} \), we need to convert the units and solve for \( r \), the radius of the atom. This yields \( r = 9.6 \times 10^{-11} \, \text{m} \).

Final Answer: \( 9.6 \times 10^{-11} \, \text{m} \).