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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

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Question

From the relation R0A1/3, where R0 is a constant and 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:

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

`:. 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.

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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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