Question

The radius of a nucleus of mass number 125 is

• A. \(6.0\ \text{fm}\)
• B. \(30\ \text{fm}\)
• C. \(72\ \text{fm}\)
• D. \(150\ \text{fm}\)

Hint:

Use \[ R=R_0A^{1/3} \] with \[ R_0=1.2\ \text{fm}. \] Whenever \(A\) is a perfect cube, the calculation becomes very quick.

Answer 1

The Correct Option is A

Concept: The empirical formula for nuclear radius is \[ R=R_0A^{1/3}, \] where \[ R_0=1.2\ \text{fm} \] and \(A\) is the mass number. This relation shows that nuclear radius increases with the cube root of the mass number.

Step 1: Write the given data. Given, \[ A=125. \] Using \[ R=1.2A^{1/3}. \]

Step 2: Evaluate \(A^{1/3}\). Since \[ 125=5^3, \] therefore \[ 125^{1/3}=5. \]

Step 3: Calculate the nuclear radius. Substituting into the radius formula, \[ R=1.2\times5. \] Thus, \[ R=6.0\ \text{fm}. \] Hence, \[ \boxed{R=6.0\ \text{fm}}. \] Therefore, the correct answer is \[ \boxed{\text{(A)}}. \]