3. Energetics Flashcards
What is amu?
Atomic mass unit
1 amu = 931.5 MeV/c^2 or 931.5 MeV
12-C used as reference nucleus
12-C has 12 amu
What is A Z and X when writing these equations?
A is the atomic mass which is protons + neutrons
Z is the atomic number which is unique to elements and puts them on the periodic table
X is the element
What is Q value?
Sum of internal energies of bodies in the initial state minus that of the bodies in the final state
Positive Q = exoergic process
Negative Q = endoergic process
Q= Σm(initial) - Σm(final)
Keep to 3 or 4 sig figs
What are the 3 types of beta decay?
β- decay
β+ decay
Decay by electron capture from atomic shells
How to find the Q value for β- decay?
(A,Z) X -> (A,Z+1) X’ + β- + v/ (antineutrino)
Q= [M(X) - M(X’)] x 931.5 MeV
Get the mass numbers from table given
If this value is greater than zero the decay can proceed (doesn’t mean it will)
How do we find the Q value for β+ decay (positron emission)?
What about electron capture (EC)?
(A,Z) X -> (A,Z-1) X’ + β+ + v (antineutrino)
Q= [M(X) - M(X’)] x 931.5 MeV - 1.022
Get the mass numbers from table given
If greater than 0, β+ emission possible
If [m(X) - m(X’)] x 931.5 < 1.022 but positive, electron capture can occur but not β+ emission
If [m(X) - m(X’)] x 931.5 > 1.022, both electron capture and β+ emission can occur
How do you find Q excitation?
Qex = Qgs - Eex
Qgs is found from the Q value for mass differences
Qex = [m(X)-m(X’)]x931.5 - Eex
Eex = Tex Tex= Qex(m(X’))/m(X)
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How to find kinetic energy of alpha particle in alpha decay?
Tα= Qgs (m(X’)) / m(X)
How to find Q value for alpha decay?
(A,Z) X -> (A-4,Z-2) X’ + (4,2) He
Q= [m(X) - m(X’) - m(He)] x 931.5 MeV
Get mass values from table given
How do you find neutron separation energy?
Sn is the minimum value of Ex
(A, Z) = (A-1, Z) + n
Sn = M(A-1, Z) - M(A, Z) + 8.071 MeV
How to find the proton separation energy?
(A, Z) = (A-1, Z-1) + p
Sn = M(A-1, Z-1) - M(A, Z) + 7.289 MeV
How to find alpha separation energy?
(A, Z) = (A-x, Z-y) + (x, y)
Sα= M(A-4, Z-2) + Mα - M(A, Z)
Sα= M(A-x, Z-y) + M(x,y) - M(A, Z)
What happens to Z when there’s e-?
What happens to Z when there’s e+?
e- -> Z=-1
e+ -> Z= +1
How do we find max kinetic energy of a product with a positive Q value?
A + B -> C + D
Tc(max) = (Q+T) Md/(Ma+Mb)
Where T is given energy in MeV
How to find the energy threshold?
A + B -> C + D
Ethreshold= |Q| x (Ma + Mb)/Mb
Where b is target and a is projectile
