Physics · nuclei · NEET
Two only. Nuclear radius R = R0 A^(1/3), where R0 = 1.2 fm (1 fm = 10^-15 m) and A is the mass number. Nuclear density is constant, about 2.3 x 10^17 kg/m^3, and it does NOT depend on A. Reason: mass grows as A, and volume also grows as A (since R^3 is proportional to A), so density = mass/volume stays the same for every nucleus.
Mass defect: delta-m = [Z*mp + (A - Z)*mn] - M, where Z = number of protons, (A - Z) = number of neutrons, mp and mn are proton and neutron masses, and M is the actual nuclear (or atomic) mass. Binding energy: Eb = delta-m * c^2. For a quick NEET shortcut, use Eb = delta-m (in u) * 931.5 MeV. Binding energy per nucleon = Eb / A.
They are three linked constants. Decay law: N = N0 e^(-lambda t). Half-life T(1/2) = 0.693 / lambda (0.693 = ln 2). Mean life tau = 1 / lambda. Combining: T(1/2) = 0.693 * tau, so half-life is always shorter than mean life. Never mix them up in a numerical.
N = N0 * (1/2)^n, where n = t / T(1/2) is the number of half-lives passed. So after 1 half-life half is left, after 2 half-lives one-fourth is left, after 3 half-lives one-eighth is left. Activity falls the same way: R = R0 * (1/2)^n. This avoids the exponential and saves time in the exam.
Q-value = (mass of reactants - mass of products) * c^2 = delta-m (in u) * 931.5 MeV. If Q is positive, energy is released. Fission of one U-235 nucleus gives about 200 MeV. Fusion of light nuclei (like hydrogen to helium) gives energy because the products have higher binding energy per nucleon, so mass is lost and released as energy.
About 10 core formulas: nuclear radius, nuclear density (constant), mass defect, binding energy, binding energy per nucleon, mass-energy relation E = mc^2, decay law, half-life, mean life, activity, and Q-value for fission and fusion. Grouping them as SIZE, MASS, DECAY makes them easy to recall.
1 u = 931.5 MeV. This is the most used conversion in the chapter. Whenever you find a mass defect in u, just multiply by 931.5 to get the energy in MeV directly.
Yes. Nuclear density is nearly constant, about 2.3 x 10^17 kg/m^3, and does not depend on the mass number A. This is because both mass and volume increase in proportion to A, so their ratio stays fixed.
Q = delta-m * 931.5 MeV, where delta-m is the mass lost (mass of reactants minus mass of products, in u). Fission of one U-235 nucleus releases about 200 MeV; fusion of light nuclei also releases energy because binding energy per nucleon rises.
N = N0 * (1/2)^n, where n = t / T(1/2) is the number of half-lives that have passed. The same (1/2)^n factor also applies to activity, so you rarely need the full exponential in NEET numericals.
