AQA A Level Physics复习笔记8.3.5 Closest Approach Estimate

• 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