What is the radius of iodine atom (at no. `53`, mass number `126`)?

Options

A. `2.5 xx 10^(-11)m`
B. `2.5 xx 10^(-9) m`
C. `7 xx 10^(-9) m`
D. `7 xx 10^(-6) m`

Explanation

To find the radius of an iodine atom (atomic number 53), we can use the formula for the radius of an electron in the nth orbit:

\[ R_n = 0.529 \times 10^{-10} \times \frac{n^2}{Z} \]

where:
- \( R_n \) is the radius of the atom,
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number.

### Step 1: Identify the atomic number and mass number
The atomic number \( Z \) of iodine is 53. The mass number is not needed for this calculation.

### Step 2: Determine the principal quantum number \( n \)
To find \( n \), we need to look at the electron configuration of iodine. The electron configuration for iodine (I) is:

\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^5 \]

Counting the shells:
- The first shell (1s) has 2 electrons.
- The second shell (2s and 2p) has 8 electrons.
- The third shell (3s, 3p, and 3d) has 18 electrons.
- The fourth shell (4s and 4p) has 7 electrons.

The outermost electrons are in the 5th shell (4p), so the principal quantum number \( n \) for the outermost electrons is 5.

### Step 3: Substitute values into the formula
Now we can substitute \( n = 5 \) and \( Z = 53 \) into the radius formula:

\[ R_n = 0.529 \times 10^{-10} \times \frac{5^2}{53} \]

Calculating \( 5^2 \):

\[ 5^2 = 25 \]

Now substituting this back into the formula:

\[ R_n = 0.529 \times 10^{-10} \times \frac{25}{53} \]

### Step 4: Calculate the radius
Now we perform the division:

\[ \frac{25}{53} \approx 0.4717 \]

Now multiply this by \( 0.529 \times 10^{-10} \):

\[ R_n \approx 0.529 \times 10^{-10} \times 0.4717 \approx 0.249 \times 10^{-10} \, \text{m} \]

This can be simplified to:

\[ R_n \approx 2.49 \times 10^{-11} \, \text{m} \]

### Final Answer
The radius of the iodine atom is approximately:

\[ R_n \approx 2.49 \times 10^{-11} \, \text{m} \]