Nuclear Physics

• Rutherford's Model of the Atom
• massive nucleus
• electrons around nucleus



• Before this model
• Henri Becquerel and Pierre and Marie Curie had observed emission from atoms
• charges varied in magnitude and sign
• mass varied
• energy varied
• three types
• alpha (a) particles - most massive, positively charged, least penetrating
• beta (b) particles - lighter, negatively charged, most common
• gamma (g) particles - no mass, no charge
• An atom would be a different element after the emission than before.
• process is occurring in nucleus
• Nucleus composed of protons and neutrons
• protons contribute to charge and mass
• neutrons contribute to mass, no charge
• Electrons???
• energies expected do not match energies observed
• magnetic moment does not match
• nuclear spin
• Rutherford proposed idea of neutral particle
• Chadwick - 1932
• Notation
• 
• X
• chemical symbol
• A
• atomic mass (number of protons + neutrons)
• Z
• atomic number (number of protons), usually omitted
• N
• neutron number (number of neutrons), usually omitted
• isotope
• same atomic number, different atomic masses
• 
• isotone
• same neutron number
• 
• isobar
• same atomic mass
• 
• mirror isobars
• Z₁ = N₂, Z₂ = N₁



• 
• dependence of chemical properties on N negligible
• atomic masses measured in atomic mass units (u)
• 1 u = 1/12 the mass of the neutral Carbon-12 atom
• 1 u = 1.66055 x 10^-27 kg = 931.49 MeV/c²
• Nuclear Spin
• nucleons (protons and neutrons also have spin)



• 



• (nuclear magneton)



• 



• nucleus in a magnetic field has a potential energy equal to
• 
• this splits the energy state into two levels






• difference between the levels is 2m_pz B
• nuclear magnetic resonance (NMR)



• Stable Nuclei
• not all combinations possible
• A < 20 , roughly equal numbers of protons and neutrons
• nuclear energy levels
• filling energy levels
• even-even
• even-odd
• odd-odd
• A > 20, neutrons dominate
• Binding Energy
• mass of individual pieces is greater than the whole
• Au-197
• 79 hydrogen atoms (79 protons and 79 electrons) and 118 neutrons
• mass of the pieces
• 
• mass of the whole
• 196.966560 u
• mass difference
• 198.6406 - 196.966560 = 1.674085 u
• total binding energy
• 
• Binding Energy/Nucleon



• 



• More Examples
• Decay processes
• alpha decay



• 



• atomic mass number decreases by four
• atomic number decreases by two
• occurs because nucleus is too large



• beta decay



• 



• atomic mass number is unchanged
• atomic number increases by one
• occurs because nucleus has too many neutrons relative to protons
• positron emission



• 
• atomic mass number is unchanged
• atomic number decreases by one
• occurs because nucleus has too many protons relative to neutrons
• electron capture



• 



• atomic mass number is unchanged
• atomic number decreases by one
• occurs because nucleus has too many protons relative to neutrons
• gamma
• 
• atomic mass number is unchanged
• atomic number is unchanged
• occurs because nucleus has excess energy



• statistical process
• cannot predict when one particular nucleus will decay
• activity is defined as the rate at which the nuclei decay or the number of decays per second



• 



• the activity should be a positive quantity while the dN/dt will be negative so we add the negative sign.
• 1 becquerel = 1 Bq = 1 decay/second
• 1 curie = 1 Ci = 3.7 x 10¹⁰ decays/second = 37 Gbq
• activity of 1 gram of radium -226



• We would expect the number of decays to be proportional to the number of radioactive nuclei remaining



• 



• lambda is the constant of proportionality and does not depend on time
• minus sign is needed because N decreases with increasing t
• use this expression to find the number of nuclei left as a function of time


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• the number of radioactive nuclei will decrease with time and approaches zero as the time gets very large.
• A useful time to use to describe the activity of a sample is the time when half of the nuclei have decayed so that N = N₀/2. We call this the half-life t_1/2. The decay constant is related to the half-life.



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