It has been found that a nucleus of mass number 'A' has a radius "R = R_oA^y," where R_o = 1.2 × 10^–15 m. Here 'y' is equal to ________.

CONCEPT:

• Nuclear radius: Experimental results indicate that volume of a nucleus is proportional to its mass number
• If R is the radius of the nucleus assumed to be spherical, then its volume

​\(⇒ \frac{4}{3}\pi r^3 ∝ A\)

Or, R ∝ A^1/3

⇒ R = R_oA1/3

Where Ro = empirical constant whose value is to be found to be 1.2 × 10-15 m = 1.2 fm.

EXPLANATION:

• The nuclear size is given

⇒ R = RoA^1/3      ------- (1)

• According to the question, the nuclear size is given by 

⇒R = R_oA^y      ------- (2)

On comparing equation 1 and 2, we get

⇒ y = 1/3

So option 4 is correct.