Question

Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of ______.

Options

• 4 : 3

• `(3/4)^(1/3)`

• 1 : 1

• `(4/3)^(1/3)`

Answer 1

Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of 1 : 1.

Radius of nucleus, R = R₀`"A"^(1/3)`     ...(i)

Density of nucleus = `"Mass of nucleus"/"volume of nucleus"`

ρ = `("m"xx"A")/(4/3pi"R"^3)` Here m = mass of proton or neutron

from equation (i), we have

ρ = `"m"xx"A"/(4/3pi"R"_0^3"A")` ⇒ ρ ∝ A⁰

As a result, the density of a nucleus is independent of its mass.