Question

How to Use the gradient from an equation of Average mass vs Average radius cubed r3 to calculate the density

Answer 1

Cube each side of the equation, giving you:

R³ = r₀³A

You then need to calculate R³ and plot R³ against A. That will give you a straight line graph with a gradient of r₀³.Calculate the gradient and value of r₀(cube root of the gradient).

For density calculation:

Assuming that-

•the nucleus is spherical OR

•all nuclei have the same density OR

•that total mass is equal to the mass of constituent single nuclei (ignoring the mass difference) OR

•ignoring the gaps between nucleons

Proceeding using the density formula (i.e. rho=M/V)

where rho=density, V=4/3 (π R³)- volume of sphere, , M= mass of a nucleon.

Putting the value of V, we get rho= 3/4(M/πR³)

If A=1 then R=r₀(here to use the gradient value)

Putting the value of R in the given equation and calculate the density.