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Questions
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.
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Solution 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
Solution 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.
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