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Solution :

Assume that the nucleus is spherical. Volume of nucleus <br> `4//3 pi r^(3) = 4//3 pi [r_(0) A^(1//3)]^(3)=4//3 pi r_(0)^(3) A` <br> Mass of nuc,eus = A <br> `:.` Nuclear mass density = Mass of nucleus/Volume of nulceus <br> `=A//(4//3 pi r_(0)^(3)A)=3//4 pi r_(0)^(3)` <br> Since `r_(0)` is a constant therefore the right hand side is a constant. So, the nuclear nass density is independent of mass number. Thus, nuclear mass density is constant for different nuclei. <br> For sodium, `A=23` <br> `:.` radius of sodium nucleus, <br> `r=1.2xx10^(-15) (23)^(1//3) m=1.2xx2.844xx10^(-15) m=3.4128xx10^(-15)` <br> Volume of nucleus `=4/3 pi r^(3)` <br> `=4/3xx22/7 (3.4128xx10^(-15))^(3) m^(3)=1.66xx10^(-43) m^(3)` <br> If we neglect the mass of electrons of a sodium atom, then the mass of its nucleus can be taken to be the mass of its atom. <br> `:.` Mass of sodium nucleus `=3.82xx10^(-26) kg` <br> (Refer to Q. 2.27) <br> Mass density of sodium nucleus <br> `=("Mass of nucleus")/("Volume of nucleus")` <br> `=(3.82xx10^(-26))/(1.66xx10^(-43)) kg m^(-3)=2.3xx10^(17) kg m^(-3)` <br> Mass density of sodium atom `=4.67xx10^(3) kg m^(-3)` <br> (Refer to Q. 2.27) <br> The ratio of the mass density of sodium nucleus to the average mass density of a sodium atom is <br> `(2.3xx10^(17))/(4.67xx10^(3)) t.e., 4.92xx10^(13)` <br> So, the nuclear mass density is nearly 50 million times more than the atomic mass density for a sodium atom.