# From the Relation R = R0a1/3, Where R0 is a Constant and a is the Mass Number of a Nucleus, Show that the Nuclear Matter Density is Nearly Constant (I.E. Independent of A). - Physics

Numerical

From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

#### Solution

We have the expression for nuclear radius as:

R = R0A1/3

Where,

R0 = Constant.

A = Mass number of the nucleus

Nuclear matter density, rho = "Mass of the nucleus"/"Volume of the nucleus"

Let m be the average mass of the nucleus.

Hence, mass of the nucleus = mA

therefore rho = "mA"/(4/3  pi"R"^3) = "3mA"/(4pi ("R"_0 "A"^(1/3))^3) = (3"mA")/(4pi"R"_0^3 "A") = "3m"/(4pi"R"_0^3)

Hence, the nuclear matter density is independent of A. It is nearly constant.

Concept: Size of the Nucleus
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#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Q 21 | Page 464
NCERT Physics Part 1 and 2 Class 12
Chapter 13 Nuclei
Exercise | Q 13.21 | Page 464