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

To determine the radius of a nucleus given its mass number, we use the empirical formula for the nuclear radius:

\(R = R_0 \cdot A^{1/3}\)

where:

• \(R_0\) is a constant approximately equal to 1.2 femtometers (fm).
• \(A\) is the mass number of the nucleus.

Given in the question, the mass number \(A\) is 125. Let's calculate the radius:

\(R = 1.2 \, \text{fm} \times 125^{1/3}\)

First, we find \(125^{1/3}\):

\(125^{1/3} = 5\) (since 5³ = 125).

Substituting this value back into the formula, we get:

\(R = 1.2 \times 5 = 6.0 \, \text{fm}\)

Therefore, the radius of the nucleus with mass number 125 is 6.0 fm, which matches option 1: "6.0 fm".

Let's verify by ruling out other options:

• Option 2: 30 fm would require a mass number significantly larger than 125.
• Option 3: 72 fm is extraordinarily large, suggesting a much larger nucleus (incorrect for A = 125).
• Option 4: 150 fm is unrealistically high, suggesting an enormous mass number, which is not the case here.

Thus, the correct answer is confirmed to be: \(6.0 \, \text{fm}\).