Question

2 nuclei have their mass number in the ratio 1:3. the ratio of their nuclear densities would be

Answer 1

Answer:

2 nuclei have their mass number in the ratio 1:3. the ratio of their nuclear densities would be 1:1.

Explanation:

The radius of an atomic nucleus is dependent on the mass number (A) of the atom. The number of nucleons present in the atom is called the mass number.

The relation between the mass number and the radius of the atomic nuclei is

$R=R_{0} (A)^{\frac{1}{3} }$

where $R_{0}$ is constant, that is equal to $1.2*10^{-15} m$

R is the radius of the nucleus.

A is the mass number.

we know that the volume of the spherical nucleus(V) is

$V=\frac{4}{3}$ π$R^{3}$

substitute the value of R then we will get

$V=\frac{4}{3}$ π  $AR_{0} ^{3}$

The mass of the atomic nuclei = the mass of a nucleon × the mass number

M = A × m

Density, ρ = $\frac{M}{V}$

Substitute M and V, then we can understand that density only density independent of the mass number

∴ the ratio 1:3. the ratio of their nuclear densities would be 1:1.