Question

The radius of the nucleus of an atom whose mass number is 125 is

• A. \( 1 \times 10^{-15} \) m
• B. \( 6 \times 10^{-15} \) m
• C. \( 3 \times 10^{-15} \) m
• D. \( 16 \times 10^{-15} \) m

Hint:

For nuclear radii, remember to use the formula \( r = r_0 A^{1/3} \) where \( r_0 \approx 1.2 \times 10^{-15} \, \text{m} \) and \( A \) is the mass number.

Answer 1

The Correct Option is B

The radius \( r \) of a nucleus is given by the empirical formula: \[ r = r_0 A^{1/3} \] where \( r_0 \) is a constant with a value approximately \( 1.2 \times 10^{-15} \) m, and \( A \) is the mass number of the nucleus. For \( A = 125 \), the radius is: \[ r = 1.2 \times 10^{-15} \times (125)^{1/3} \] First, compute \( (125)^{1/3} \): \[ % Option (125)^{1/3} \approx 5 \] Therefore, \[ r \approx 1.2 \times 10^{-15} \times 5 = 6 \times 10^{-15} \, \text{m} \] Thus, the radius of the nucleus is \( 6 \times 10^{-15} \) m. Therefore, the correct answer is option (2), \( 6 \times 10^{-15} \, \text{m} \).

Answer 2

Step 1: Understanding the problem
We need to find the radius of the nucleus of an atom with mass number \( A = 125 \).

Step 2: Formula for nuclear radius
The radius \( R \) of a nucleus is given by:
\[ R = R_0 \times A^{1/3} \]
where \( R_0 \approx 1.2 \times 10^{-15} \, \text{m} \) (constant)

Step 3: Calculate the radius
\[ R = 1.2 \times 10^{-15} \times (125)^{1/3} \]
Since \( 125^{1/3} = 5 \),
\[ R = 1.2 \times 10^{-15} \times 5 = 6 \times 10^{-15} \, \text{m} \]

Step 4: Final answer
The radius of the nucleus is \( 6 \times 10^{-15} \) m.