Question

assuming a spherical shape for fluorine nucleus, calculate the radius and the nuclear density of fluorine nucleus of mass number 19.

Answer 1

Given:

Assume a spherical shape for fluorine nucleus

To find:

Calculate the radius and the nuclear density of fluorine nucleus of mass number 19.

Solution:

Radius of Nucleus :

R= R₀A^{1/3}  where R₀ = 1.2 × 10-15m

Putting the value in formula : R= 1.2 × 10-15m × (19)^{1/3} = 3.2 × 10-15m

Density of  Nuclear Matter:

Volume of nucleus =  (4/3) π R³ = 4/3 × 3.14 × ( 3.2 × 10-15m)³ = 4/3 × 3.14 × 32.77 × 10-45m³ = 1.38 × 10-43m³

Density of nucleus  =  Mass / Volume  

The mass of the nucleus is 19  = 3.15 × 10-26 kg. (mass of 1 mole or 6.023 × 1023 = 19g

∴ The mass of 1 nucleus will be 19/6.023 × 1023 g = 3.15 x 10-23 g = 3.15 × 10-26 kg )

Density = 3.15 × 10-26 kg./1.38  10-43m³ = 2.28  10^{17} kg/m³

Therefore, the radius and the nuclear density of fluorine nucleus of mass number 19 are 3.2 × 10-15m  and 2.28  10^{17} kg/m³.