#### Question

From the relation *R *= *R*_{0}*A*^{1}/^{3}, where *R*_{0} 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 *= *R*_{0}*A*^{1}/^{3}

Where,

*R*_{0} = 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*

`:. rho = mA/(4/3 piR^3) = "3mA"/(4pi (R_0 A^(1/3))^3) = (3mA)/(4piR_0^3 A) = "3m"/(4piR_0^3)`

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

Is there an error in this question or solution?

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Solution 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). Concept: Size of the Nucleus.

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