The unit of length conventent on the nuclear scale is a fermi : `1f = 10^(-15)`m. Nuclear sized obey roughly the following empirical relation:
`r = r_(0)A^(1//3)`
Where r is the radius of the nucleus, A its mass number, and `r_(0)` is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise . 2.27.

Explanation

Radius of nucleus `r=r_(0)A^(1/3)`
where `r_(0)`= constant and A =atomic mass
Valume of nucleus `V=(4)/(3)pir^(3)`
`=(4)/(3)pi(r_(0)A^(1/3))^(3)`
`=(4)/(3)pir_(0)^(3).A`
mass o f nucleus M=mA
density of nucleus `rho=(M)/(V)`
`=(mA)/((4)/(3)piAr_(0)^(3))`
`=(3m)/(4pir_(0)^(3))`
`=(3xx1.66xx10^(-27))/(4xx3.14xx(1.2xx10^(-15))^(3))`
`=0.22945xx10^(18)`
`~~2.29xx10^(17)kgm^(-3)`
density of all nuclei is same, so diensity of sodium nucleus `=2.29xx10^(17)kgm^(-3)`
From 2.27, average density of sodium atom is `584kgm^(-3)`.
`:.("Desnity of sodium nucleus "rho)/("Density of sodium atom" rho.)=(2.29xx10^(17))/(584)`
`=0.00392xx10^(17)`
`~~0.39xx10^(15)`
`~~10^(15)`
Density of nucleus is `10^(15)` times density of atom.