6 Mass-Energy Equivalence

8/13/2019 6 Mass-Energy Equivalence

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Mass-Energy

Equivalence


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Work is required to remove a nucleon from

a stable nucleus because of the strongnuclear force

The binding energy of a nucleus is the

energy required to separate all of its

nucleons and move them infinitely far

apart


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The maximum binding energy per nucleon is

between A =50 and A =74 (most stable)


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Comparison of Atomic & Nuclear

binding energy


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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


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the binding energy is related to the mass

defect by the equation E = mc2


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Example

Determine the mass defect and binding

energy of an alpha particle.


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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


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mass defect = proton mass + neutron

mass - mass = 0.03 x 10-27 kg E = mc2

E = (0.03 x 10-27

kg)(3.00 x 108

m/s)2

E = 2.70 x 10-12 J


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in nuclear reactions, mass is converted to

energy or energy is converted to mass

Conservation of mass-energyprinciple


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Example

Calculate the energy produced in the reaction

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


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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


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E = mc2

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

E = 2.59 x 10-12 J

in the form of kinetic energy of products


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STS

In a CANDU reactor, 1 kg of fuel (natural

uranium) produces 3.4 x 105 MJ of heatthat is converted to electricity

in oil and coal power plants 1 kg of fuel

produces about 4 MJ of heat


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Pair Production

a very high energy photon may create

matter

The process must produce 2 particleswhose total charge is zero, since charge &

momentum must be conserved.


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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


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Bubble chamber track

Neutral particles do not leave a

track


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Example

A 8.50 x 1020 Hz photon produces an

electron and an anti-electron. Determinethe total kinetic energy of the particles.

Conservation of Mass-Energy!!!


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6 Mass-Energy Equivalence

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