Energy-Momentum Relation (Edexcel International A Level Physics)

This is a common derivation, so make sure you're comfortable with deriving this from scratch! Think carefully about the algebra on each step.

Calculate the kinetic energy, in MeV, of an alpha particle which has a momentum of 1.1 × 10^–19 kg m s^–1.

Use the following data:

• Mass of a proton = 1.67 × 10^–27 kg

• Mass of a neutron = 1.67 × 10^–27 kg

Answer:

Step 1: Write the energy-momentum relation

• The energy-momentum relation is given by E_k = 

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 m_α = 2m_p + 2m_n, where m_p and m_n is the mass of a proton and neutron respectively

• So m_α = 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

E_k = 

E_k = = 9.1 × 10^–13 J

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

1 MeV = 1.6 × 10^–13 J

• Therefore:

9.1 × 10^–13 J = MeV = 5.7 MeV

Calculations with the energy-momentum equation often require changing units, especially between eV and J due to it commonly being used for particles. Remember that 1 eV = 1.60 × 10^-19 J. Therefore

eV → J = × (1.60 × 10^-19)

J → eV = ÷ (1.60 × 10^-19)

The prefix 'mega' (M) means × 10⁶ therefore, 1 MeV = (1.60 × 10^-19) × 10⁶ = 1.60 × 10^-13