Physics · nuclei · NEET
Write density = mass / volume. Mass of nucleus is about A times the nucleon mass m, so mass = A x m. Volume is (4/3) pi R^3, and since R = R0 A^(1/3), we get R^3 = R0^3 A. So volume = (4/3) pi R0^3 A. Now density = (A m) / ((4/3) pi R0^3 A). The A on top and the A on bottom cancel, leaving density = m / ((4/3) pi R0^3), which has NO A in it. That is why it is the same for all nuclei.
For a nucleus, both mass and volume grow in the same way with A, so density stays fixed. For a whole atom this is not true: the atomic radius does not follow R0 A^(1/3), and electron shells fill up in a complicated way, so atomic volume does not grow in step with atomic mass. NCERT states this directly: the density of nuclear matter is independent of size, but the mass density of the atom does not follow this rule.
About 2.3 x 10^17 kg/m3. Compare this with water at 10^3 kg/m3. So nuclear matter is roughly 10^14 (a hundred trillion) times denser than water. NCERT notes that matter inside a neutron star has a similar density, meaning a neutron star is like one giant nucleus.
No. A bigger nucleus (larger A) is physically larger, because R = R0 A^(1/3). What stays constant is density, not size or mass. Think of drops of the same liquid: a big drop and a small drop have different sizes and masses but the SAME density. NCERT calls nuclei like drops of a liquid of constant density.
A common slip. The radius is R = R0 A^(1/3), so radius is proportional to A^(1/3). Volume goes as R^3, and (A^(1/3))^3 = A^1 = A. So volume is proportional to A (the power 1/3 and the power 3 multiply to 1). Volume is NOT proportional to A^3.
Nuclear density is about 2.3 x 10^17 kg/m3. It is the same for all nuclei, from light ones to heavy ones.
Because mass is proportional to A and volume is also proportional to A (since R = R0 A^(1/3) gives R^3 proportional to A). In density = mass/volume, the A cancels, so density has no A dependence.
Yes. NCERT states nuclear density is a constant, independent of A, for all nuclei. Different nuclei behave like drops of one liquid of constant density.
Nuclear density (about 2.3 x 10^17 kg/m3) is roughly 10^14 times the density of water (10^3 kg/m3). This is why nuclear matter is called extremely dense.
A neutron star. NCERT notes that matter in a neutron star has a density comparable to nuclear density, so a neutron star is like one huge nucleus.
