Question

The radius of a nucleus of mass number 125 is:

• A. 6.0 fm
• B. 30 fm
• C. 72 fm
• D. 150 fm

Hint:

Use \( R = 1.3 A^{1/3} \, \text{fm} \). Remember: \( 125^{1/3} = 5 \) (perfect cube → quick calculation).

Answer 1

The Correct Option is A

Concept: The radius of a nucleus is given by the empirical formula: \[ R = R_0 A^{1/3} \] Where:

\( R_0 \approx 1.3 \, \text{fm} \)
\( A \) = mass number

Step 1: Substitute the given mass number. \[ A = 125 \] \[ R = 1.3 \times 125^{1/3} \]
Step 2: Evaluate cube root. \[ 125^{1/3} = 5 \]
Step 3: Calculate radius. \[ R = 1.3 \times 5 = 6.5 \, \text{fm} \] Using the commonly accepted approximation \( R_0 \approx 1.2 \, \text{fm} \): \[ R = 1.2 \times 5 = 6.0 \, \text{fm} \]
Step 4: Choose the closest option. The nearest value is \( 6.0 \, \text{fm} \).