Physics · nuclei · NEET
A is the mass number, which is the total number of nucleons (protons + neutrons) in the nucleus. It is NOT the atomic number Z. For example, for iron Fe-56, A = 56, so R = 1.2 x (56)^(1/3) fm. Always use A, the top number in the nuclide symbol, not Z.
R0 = 1.2 x 10^-15 m = 1.2 fm (femtometre). One femtometre, also called one fermi, equals 10^-15 m. R0 is a constant found from experiments, and it is the same for every nucleus. In some books R0 is written as 1.1 to 1.3 fm, but NCERT and NEET use 1.2 fm.
Because experiments show the volume of a nucleus is directly proportional to A. Volume of a sphere is (4/3)piR^3, so R^3 is proportional to A, which means R is proportional to A^(1/3). The cube root simply comes from taking the cube root of volume to get radius.
Step 1: write A of the nucleus. Step 2: find the cube root of A. Step 3: multiply by R0 = 1.2 fm. Example for A = 27 (aluminium): cube root of 27 = 3, so R = 1.2 x 3 = 3.6 fm. Pick A values that are perfect cubes (8, 27, 64, 125, 216) because they make the cube root easy in exams.
The RADIUS R is proportional to A^(1/3). The VOLUME is proportional to A. Students often mix these up. If A becomes 8 times larger, the radius becomes only 2 times larger (cube root of 8 = 2), but the volume becomes 8 times larger.
Use a ratio: R1/R2 = (A1/A2)^(1/3), because R0 cancels out. For example, the ratio of radii of nuclei with A = 64 and A = 27 is (64/27)^(1/3) = 4/3. This ratio trick saves time and avoids using R0 at all.
R = R0 A^(1/3), where R is the nuclear radius, A is the mass number, and R0 = 1.2 x 10^-15 m (1.2 fm). This tells you the nucleus is a small sphere whose size depends only on the number of nucleons.
R0 = 1.2 x 10^-15 m, which is the same as 1.2 femtometre or 1.2 fermi. It is a constant that is the same for all nuclei.
The radius of a nucleus is about 10^4 (ten thousand) times smaller than the radius of an atom. This means the nucleus takes up only about 10^-12 of the atom's volume, so an atom is almost empty space.
Yes. Since R^3 is proportional to A, the volume is proportional to A. Mass is also proportional to A, so density (mass/volume) stays constant and does not depend on A. This is why all nuclei behave like a liquid drop of the same density, about 2.3 x 10^17 kg/m^3.
A femtometre (fm), also called a fermi, is a unit of length equal to 10^-15 metre. Nuclear sizes are measured in fermi because a nucleus is only a few fermi across.
