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Question

Why nuclear density is not dependent on the mass number?


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Solution

Nuclear density:

  • Nuclear density is the density of the nucleus of an atom.
  • It is the mass-to-volume ratio inside the nucleus.

Relationship between radius and mass number

  • The radius (size) R of nucleus is related to its mass number (A) as
  • R=R0A1/3where R0=1.1×10-15m
  • If m is the average mass of a nucleon, then
  • mass of nucleus = mA, where A is the mass number

Find the volume of the nucleus

Volumeofnucleus=43πR3=43π(R0A1/3)3=43πR03A

Finding the density of the nucleus

Let nuclear Density be ρN

ρN=massvolumeρN=mA43πR03A

ρN=m43πR03

Since the formula of nuclear density is free of A(mass number).

Hence we can conclude that nuclear density is not dependent on the mass number.


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