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

Options

A. `2.5xx10^(-11) m`
B. `2.5 xx10^(-9) m`
C. `7xx10^(-9) m`
D. `7xx10^(-6) m`

Answer

To find the radius of the iodine atom with atomic number 53 and mass number 126, we can use the formula for the radius of an atom:

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

Where:
- \( R_n \) is the radius of the atom in meters,
- \( n \) 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 126, but we do not need it to find the radius.

### Step 2: Determine the Principal Quantum Number \( n \)
- The electronic configuration of iodine is \( 2, 8, 18, 18, 7 \).
- The highest energy level (or shell) corresponds to the outermost electrons, which is the 5th shell. Therefore, \( n = 5 \).

### Step 3: Substitute Values into the Formula
Now we can substitute the values of \( n \) and \( Z \) into the formula:

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

### Step 4: Calculate \( R_n \)
1. Calculate \( 5^2 \):
\[ 5^2 = 25 \]

2. Substitute this back into the equation:
\[ R_n = \frac{0.529 \times 10^{-10} \times 25}{53} \]

3. Calculate the numerator:
\[ 0.529 \times 25 = 13.225 \times 10^{-10} \]

4. Now divide by 53:
\[ R_n = \frac{13.225 \times 10^{-10}}{53} \]

5. Performing the division:
\[ R_n \approx 2.5 \times 10^{-11} \text{ meters} \]

### Step 5: Convert to Appropriate Units
Since the radius is often expressed in picometers (pm) or angstroms (Å), we can convert:
- \( 1 \text{ meter} = 10^{10} \text{ angstroms} \)
- Therefore, \( R_n \approx 2.5 \times 10^{-11} \text{ m} = 25 \text{ pm} \) or \( 0.25 \text{ Å} \).

### Final Answer
The radius of the iodine atom is approximately \( 2.5 \times 10^{-11} \text{ meters} \).

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