Edexcel A Level Physics:复习笔记6.6 Energy-Momentum Relation

• The equation for calculating the kinetic energy Ek of a particle m moving at velocity v is given by:

• 
• The formula for the momentum p of the same particle is:
• 

• Combining these gives an equation that links kinetic energy to momentum, called the energy-momentum relation
  • Firstly, substituting the equation for velocityinto the equation for kinetic energy gives:

• • Multiplying brackets out and simplifying gives:
  • 

• Therefore the energy-momentum is presented as:

• Where:
  • Ek = kinetic energy (J)
  • p = momentum (kg m s-1)
  • m = mass (kg)

• The energy-momentum relation is particularly useful for:
  • Calculations involving the kinetic energy of subatomic particles travelling at non-relativistic speeds (i.e. much slower than the speed of light)
  • Projectiles and collisions involving large masses

Step 1: Write the energy-momentum relation

• • The energy-momentum relation is given by

Step 2: Determine the mass of an alpha particle

• • An alpha particle is comprised of two protons and two neutrons
  • Therefore, the mass of an alpha particle mα = 2mp + 2mn, where mp and mn is the mass of a proton and neutron respectively
  • So mα = 2(1.67 × 10–27) + 2(1.67 × 10–27) = 6.68 × 10–27 kg

Step 3: Substitute the momentum and the mass of the alpha particle into the energy-momentum relation

Step 4: Convert the value of kinetic energy from J to MeV

1 MeV = 1.6 × 10–13 J

• • Therefore: