(a) Classify the following six nuclides into (i) isotones, (ii) isotopes, and (iii) isobars :

        _{6}^{12}\textrm{C},\; _{2}^{3}\textrm{He},\; _{80}^{198}\textrm{Hg},\; _{1}^{3}\textrm{H},\; _{79}^{197}\textrm{Au},\; _{6}^{14}\textrm{C}

(b) How does the size of a nucleus depend on its mass number? Hence explain why the density of nuclear matter should be independent of the size of the nucleus.

 

 
 
 
 
 

Answers (1)
S safeer

(a) Classification of nuclides are as follows;-

(i) isotopes\; ;\; _{6}^{12}\textrm{C}\; and\; _{6}^{14}\textrm{C}

(ii) isobars\; ;\; _{2}^{3}\textrm{He}\; and\; _{1}^{3}\textrm{H}

(iii) isotones\; ;\; _{80}^{198}\textrm{Hg}\; and\; _{79}^{197}\textrm{Au}

(c) The radius of the nucleus having mass number A is given as ;

        R=r_{0}(A)^{\frac{1}{3}}

Where, A= mass no.

            R= radius

            r_{0}= constant value

Such that, the volume of the nucleus;- 

=\frac{4}{3}\pi R^{3}

 =\frac{4}{3}\pi \times r_{0}^{3}\times A^{\frac{1}{3}\times 3}

 =\frac{4}{3}\pi r_{0}^{3} A

  If m be the average mass of a nucleon, then the mass of nucleus =mA

\therefore the nuclear density

=\frac{mass }{volume }=\frac{mA}{\frac{4}{3}\pi (r_{0}^{3})\times A}=\frac{3m}{4\pi (r_{0})^{3}}

Hence, nuclear density is independent of the size of the nucleus.

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