Question

Answer the following question.

Show that the density of the nucleus is independent of its mass number A.

Show that nuclear density in a given nucleus is independent of mass number A.

Answer 1

Density of the nucleus = `(\text { mass of nucleus})/(\text { volume of nucleus})`

Mass of the nucleus = A amu = A × 1.66 × 10^-27 kg

Volume of the nucleus = `4/3πR^3 = 4/3π(R_0A^(1/3))^3 A =4/3πR_0^3 A`

Thus, density = `(Axx1.66 xx10^(-27))/((4/3πR_0^3)A)` = `(1.66 xx 10^-27)/((4/3πR_0^3)`

which shows that the density is independent of mass number A.

Using R₀ = 1.1 × 10^-15 m and density = 2.97 × 10¹⁷ kg m^-3

Answer 2

Density = `("p") = "m"/"v"`

R = `"R"_0("A")^(1/3)`

Volume = `(4)/(3)"πR"^3`

Volume of atom = `(4)/(3)π ("R"_0 "A"^(1/3))^3`

= `(4)/(3)π"R"_0^3"A"`

Density = `"mass"/"volume"`

 `"p" = ("m"."A")/((4)/(3) "πR"_0^3 "A")`

`"p" = ("m")/((4)/(3) "πR"_0^3)`

m = mass of proton

It shows independence in mass.