Distance Of Closest Approach — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Distance of Closest Approach Used in Rutherford Scattering to estimate the upper limit of the radius of the nucleus. Apply conservation of mechanical energy: Total Initial Energy = Total Final Energy. At infinite distance, Potential Energy is zero; total energy is purely Kinetic Energy (K). At r 0, the alpha particle momentarily stops; Kinetic Energy is zero; total energy is purely Electrostatic Potential Energy (U). U = k (q1 q2) / r 0, where q1 = 2e (alpha particle) and q2 = Ze (nucleus). K = k (2Ze 2) / r 0 and solve for r 0. Assumes a head-on collision (impact parameter b = 0). Assumes the nucleus remains stationary due to its much larger mass compared to the alpha particle. Assumes only electrostatic interaction (ignoring strong nuclear force until distance is very small). Thinking r 0 is the actual radius of the nucleus (it is usually larger than the actual radius). Forgetting the factor of 2 in the numerator (alpha particles have 2 protons). Using mass instead of atomic number for Z.