It has been found that a nucleus of mass number 'A' has a radius

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

A. 1/2

B. 2

C. 3

D. 1/3

Please scroll down to see the correct answer and solution guide.

Right Answer is: D

SOLUTION

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 ∝ A1/3

⇒ R = RoA1/3

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 = RoA1/3      ------- (1)

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

⇒R = RoAy      ------- (2)

On comparing equation 1 and 2, we get

⇒ y = 1/3

So option 4 is correct.

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