Mass-Energy Equivalence - Linville Mass-Energy...Mass-Energy Equivalence ... • the binding energy is related to the mass defect by the ... energy or energy is converted to mass •

Mass-Energy Equivalence

• Work is required to remove a nucleon from a stable nucleus because of the strong nuclear force

• The binding energy of a nucleus is the energy required to separate all of its nucleons and move them infinitely far apart

The maximum binding energy per nucleon is between A =50 and A =74 (most stable)

Comparison of Atomic & Nuclear binding energy

Mass Defect

• The mass of a nucleus is always less than the mass of all the separate nucleons (protons and neutrons)

• this difference in mass is called the mass defect

• the binding energy is related to the mass defect by the equation ΔE = Δmc2

Example

• Determine the mass defect and binding energy of an alpha particle.

Solution• alpha particle mass (2 protons, 2 neutrons) =

6.65 x 10-27 kg (data sheet)

• mass of 2 protons = 2 x 1.67 x 10-27 kg = 3.34 x 10-27 kg

• mass of 2 neutrons = 2 x 1.67 x 10-27 kg = 3.34 x 10-27 kg

• total mass of separate nucleons = 6.68 x 10-27

kg

• mass defect = proton mass + neutron mass - α

mass = 0.03 x 10-27 kg

• ΔE = Δmc2

• ΔE = (0.03 x 10-27 kg)(3.00 x 108 m/s)2

• ΔE = 2.70 x 10-12 J

• in nuclear reactions, mass is converted to energy or energy is converted to mass

• Conservation of mass-energy principle

Example

• Calculate the energy produced in the reaction

2H mass = 3.34341 x 10-27 kg3H mass = 5.00661 x 10-27 kg

Solution

• Total mass of reactants = 8.35002 x 10-27 kg

• The total mass of the products = 8.3212x10-27 kg

• Mass defect • =8.35002x10-27 kg – 8.3212x10-27 kg• = 2.882 x 10-29 kg

• ΔE = Δmc2

• ΔE = (2.882 x 10-29 kg)(3.00 x 108 m/s)2

• ΔE = 2.59 x 10-12 J

• in the form of kinetic energy of products

STS

• In a CANDU reactor, 1 kg of fuel (natural uranium) produces 3.4 x 105 MJ of heat that is converted to electricity

• in oil and coal power plants 1 kg of fuel produces about 4 MJ of heat

Pair Production

• a very high energy photon may create matter

• The process must produce 2 particles whose total charge is zero, since charge & momentum must be conserved.

• A particle and its antiparticle (antimatter) are often produced (i.e. an electron and antielectron) have the same mass and other properties, but opposite signs

Bubble chamber trackNeutral particles do not leave a track

Example

• A 8.50 x 1020 Hz photon produces an electron and an anti-electron. Determine the total kinetic energy of the particles.

• Conservation of Mass-Energy!!!

Solution• photon energy = energy to make particles + Ek

• Ephoton = Eelectron + Eantielectron + Ek

• hf = mc2 + mc2 + Ek

• Ek =(6.63x10-34J•s)(8.50x1020) - 2(9.11x10-31kg)c2

• = 4.00 x 10-13 J