The radius of a nucleus of a mass number `A` is directly proportional to.

Options

A. `A^(3)`
B. `A`
C. `A^(2//3)`
D. `A^(1//3)`

Explanation

To solve the question regarding the relationship between the radius of a nucleus and its mass number \( A \), we can follow these steps:

### Step 1: Understand the relationship
The radius of a nucleus is found to be related to its mass number \( A \). The empirical formula that describes this relationship is:

\[ r = R_0 A^{1/3} \]

where \( R_0 \) is a constant (approximately \( 1.2 \) femtometers).

### Step 2: Identify the proportionality
From the formula \( r = R_0 A^{1/3} \), we can see that the radius \( r \) is directly proportional to \( A^{1/3} \). This means that if we increase the mass number \( A \), the radius \( r \) will increase as well, following the cube root relationship.

### Step 3: Conclusion
Thus, we conclude that the radius of a nucleus of mass number \( A \) is directly proportional to \( A^{1/3} \).

### Final Answer
The radius of a nucleus of mass number \( A \) is directly proportional to \( A^{1/3} \).

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