The nuclear radius can be estimated from the closest approach of an alpha particle: at the

Nuclear & Particle Physics - OCR A-Level Physics

The nuclear radius can be estimated from the closest approachThe minimum distance between an alpha particle and a nucleus, found by equating kinetic energy to electrostatic potential energy. of an alpha particle: at the distance of closest approach, all kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. has been converted to electrical potential energyThe capacity to do work. Measured in joules (J)..
High-energy electron diffractionThe wave-like scattering of electrons when passed through a crystal lattice, providing evidence for wave-particle duality. gives a more precise measurement. The first minimum of the diffraction pattern occurs at sin θ ≈ 0.61λ/R.

r = r_0 A^{1/3}

Since r ∝ $A^{1/3}$, the volume V ∝ r³ ∝ A. This means nuclear densityMass per unit volume of a material. Measured in kg m⁻³. is approximately constant for all nuclei.
Nuclear densityMass per unit volume of a material. Measured in kg m⁻³. ≈ 10¹⁷ kg m⁻³ - about 10¹⁴ times denser than ordinary matter.
Electron diffraction is preferred over alpha scattering because electrons interact via the electromagnetic forceThe fundamental force between charged particles, responsible for binding electrons to nuclei and chemical bonding. only (not the strong force), giving a cleaner measurement of the chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). distribution.

Common Mistake MEDIUM

Wrong: $r = r_{0} A means$ the radius is proportional to A.
Right: r = r₀A^(1/3) - the radius is proportional to the cube root of A. Volume is proportional to A, not radius.