• The Coulomb equation can be used to give an estimate for the radius of a nucleus
• When the alpha particle reaches its closest approach (to the nucleus), all of its kinetic energy has been converted to electric potential energy
• Initially, the alpha particles have kinetic energy equal to:

• The electric potential energy between the two charges is equal to:

• At this point, the kinetic energy?Ek?lost by the α particle approaching the nucleus is?equal?to the potential energy gain?Ep, so:

• Where:
  • m?= mass of an α particle (kg)
  • v?= initial speed of the α particles (m s–1)
  • q?= charge of an α particle (C)
  • Q?= charge of the nucleus being investigated (C)
  • r?= the radius of closest approach (m)
  • ε0?=?permittivity of free space

   

Step 1: List the known quantities

• • Mass of an α particle,?m?= 4u = 4 × (1.66 × 10–27) kg
  • Speed of the α particle,?v?= 2.55 × 107?m s–1
  • Charge of an α particle,?q?= 2e?= 2 × (1.6 × 10–19) C
  • Charge of an aluminium nucleus,?Q?= 13e?= 13 × (1.6 × 10–19) C
  • Permittivity of free space, ε0?= 8.85 × 10–12?F m–1

   

Step 2: Write down the equations for kinetic energy and electric potential energy

Step 3: Rearrange for distance,?r

Step 4: Calculate the distance,?r

r?= 2.77 × 10–15?m