Question

If r₁ and r₂ are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio \((\frac{r_1}{r_2})\)is
1. \(\frac{64}{125}\)
2. \(\sqrt{\frac{64}{125}}\)
3. \(\frac{5}{4}\)
4. \(\frac{4}{5}\)

Answer 1

Correct Answer - Option 4 : \(\frac{4}{5}\)

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 f m. (It is measured by using experiments in the laboratory)

EXPLANATION:

Given - A₁ = 64 and A₂ = 125

• The relation between the radius and mass number is given by

⇒ R = RoA1/3

• For radii of the atomic nuclei of mass numbers 64

⇒ r₁ = Ro(64)1/3 = 4R_o      ------ (1)

• For radii of the atomic nuclei of mass numbers 125

⇒ r2 = Ro(125)1/3 = 5Ro      ------ (2)

On dividing equation 1 and 2, we get

\(\Rightarrow \frac{r_1}{r_2}=\frac{4}{5}\)