Question

Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number A.

Answer 1

To find the density of nucleus of an atom, we have an atom with mass number lets say A. (Here, we are neglecting mass of the orbital electrons)

Mass of the nucleus of the atom of the mass number A.

= A a.m.u

= A × 1.660565 × 10⁻²⁷ kg

Let radius of nucleus is R.

Then,volume of nucleus, `=4/3 piR^3`

`= 4/3 pi (R_0A^(1/3))^3`

`=4/3 piR_0^3A`

Now, we know R₀ = 1.1 × 10⁻¹⁵ m

∴Volume of nucleus` 4/3 pi (1.1 xx 10^-15)^3 xx Am^3`

Density of the nucleus

`δ = (\text { Mass of nucleus})/(\text { Volume of nucleus})`

`= (A xx 1.6605 xx 10^-27)/(4/3pi (1.1 xx 10^-15)^3 xx A)`

`= 2.97 xx 10^17 kgm^-3`

Thus, we can see the density of nuclei is independent of the mass number and is constant for all nuclei.