Nuclear Chemistry and Mass-Energy Relationships

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Nuclear Chemistry and Mass-Energy Relationships

• Chapter 3 Part 2

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Mass Excess or Mass Defect

• ? M A nuclidic mass mass number
• Example
• Calculate mass excess in MeV for 14C. The
  nuclidic mass of 14C is 14.00324 daltons.
• ? M A 14.00324 14 3.24 x 10-3 daltons
  3.24 x 10-3 daltons x 931.5 MeV/dalton 3.02
  MeV

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Energy Changes in Nuclear Reactions

• Q-value
• Q (Smassesreactants-Smassesproducts) x 931.5
  MeV/daltons
• Q S ?reactants - S ?products
• Q-value calculator http//www.nndc.bnl.gov/qcalc/
• Atomic Mass Data Centerhttp//www.nndc.bnl.gov/am
  dc/

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Q-value
Energy released in a nuclear reaction (gt 0 if
energy is released, lt 0 if energy is used)
Example The sun is powered by the fusion of
hydrogen into helium
4p ? 4He 2 e 2ne
Mass difference dMreleased as energydE dM x c2
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Binding Energy

• E (MeV) Masses of reactants Masses of
  products) 931.5 MeV/dalton

BE Zmp Nmn m(AX) Zmec2 if
using atomic masses -
BE ZmH Nmn m(AX)c2
(Remember 1 u 1 dalton 931.5 MeV/c2
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Binding Energy
Energy that is released when a nucleus is
assembled from neutrons and protons
mp proton mass, mn neutron mass, m(Z,N)
mass of nucleus with Z,N

• B 0 for H, otherwise B gt 0
• 2D1 - deteriumBE (1.007825 1.008665 -
  2.0141) x 931.481 MeV 2.226 MeV
• 4He2BE (21.007825 21.008665 - 4.002603) x
  931.481 MeV 28.30 MeV
• 238U146BE (921.007825 1461.008665 -
  238.0289) x 931.481 MeV 1822.06 MeV

The more nucleons packed into a nucleus, the more
energy is released, and thus the higher the
binding energy.
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Binding Energy per Nucleon
Source http//hyperphysics.phy-astr.gsu.edu/
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Energy Changes in Radioactive Decay

• Alpha Decay
• 252Cf ? 248Cm a
• Q ?Cf (?Cm ?a) 76.030 (2.424 67.388)
  6.22 MeV

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Energy Changes in Radioactive Decay

• Negatron Decay
• 32P ? 32S e- antineutrino Q
• Q ?P- ?S -24.305 (-26.016) 1.711 MeV
• Positron Decay
• 26Al ? 26Mg e atomic electron neutrino Q
• Q ?(26Al) ?(26Mg) 2me
• -12.210 (- 16.214 2(0.511)) 2.982 MeV

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Closed-Cycle Decay for Mass-Energy Calculations

• QPu?U QU?Np QPu ? Am QAm ?Np
• QU?Np QPu ? Am QAm ?Np- QPu?U
• QU?Np 0.0208 5.49 -4.90 0.61 MeV

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Semiempirical Binding Energy Equation

• a) Volume
• BE/A 8 MeV, so BE 8A or BE ? A
• ? avA
• b) Surface
• nuclei on surface have fewer neighbors volume
  term will over-estimate BE
• surface area of sphere 4pR2
• so ? R2
• ? (r0A1/3)2
• ? A2/3
• asA2/3
• c) Coulomb
• Coulomb repulsion of protons each proton
  repels all others
• Z protons repelling (Z 1) protons
• estimate using Coulomb energy for a sphere
  

Collect constants into one ac 0.72 MeV
acZ(Z-1)A-1/3
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Semiempirical Binding Energy Equation

• d) Symmetry
• Light stable nuclei have NZ, heavy nuclei have
  NgtZ
• Too many protons, unstable too many neutrons,
  unstable
• asym(A - 2Z)2/A
• e) Pairing
• Preferred BE for even Z, N
• Pairing energy d
• d apA-3/4 even Z and even N
• d 0 odd Z, even N OR even
  Z, odd N
• d -apA-3/4 odd Z and odd N

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Binding Energy
Best fit values (from A.H. Wapstra, Handbuch der
Physik 38 (1958) 1)
aV aS aC aA aP
15.85 18.34 0.71 92.86 11.46
in MeV/c2
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Nuclear Energy Surface Diagram
For a constant A
Binding energy per nucleon along const A due to
asymmetry term in mass formula
2d-displacement
valley of stability
(Bertulani Schechter)