Radioactivity, Radiation and the Structure of the atom

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1 Radioactivity, Radiation and the Structure of the atom What do you know (or can we deduce) about radioactivity from what you have learned in the course so far?

2 How can we learn about whether radioactive decay has occurred?

3 Chart of Nuclides: Not all combinations of neutrons and protons are allowed. Atomic Number Neutron Number Why do some combinations of neutrons and protons occur and not others?

4 Binding energy E=mc ; mass and energy are equivalent c= velocity of light =.9979 x cm/s 1 amu = x 10-4 g E=(1.660 x 10-4 g)(.9979 x cm/s) = 1.49 x 10-3 erg 1 ev = 1.60 x 10-1 erg 1 amu = ev Alternatively one may say that c = ev/u

5 Description ass in g ass in ev Symbol m p ass of proton x 10-4 g m n ass of neutron x 10-4 g m e ass of electron 9.1x10-8 g Note that there is a factor of ~ between the mass of an electron and a proton/neutron. Why is the mass of a proton less than the mass of a neutron?

6 Using mass tables Define: ass Defect = Δ ; This is sometimes called the ass Excess. = ( A) c units of Δ in ev Or = A + c Units of in amu abbreviated u Example: ( 4 ) = u, what is Δ? Δ = (-A)c = ( )u( ev/u) =.45 ev Likewise, if you know Δ you can calculate.

7 Taken From Nuclear Wallet cards, 5th ed J.K. Tuli (posted on class Website)

8 Chemical Atomic Weight Z = i f i i f i = relative abundance i = mass of each isotope Example: f( 63 Cu) = % ; f( 65 Cu) = % ; ( 63 Cu) = ; ( 65 Cu) = Problem: Calculate < Cu >.

9 Relativistic Effects Relativity says that if we increase the velocity of a particle, its total mass increases. This prediction is verified at accelerators. For example, for a 00 ev proton v=0.6c ; / 0 = 1.5 IN THIS COURSE WE WILL IGNORE RELATIVITY (except in a few special cases). use classical equations of motion: E = 1 0 V p = 0V expression for the kinetic energy of a particle with rest mass 0 and velocity V expression for the momentum of a particle with rest mass 0 and velocity V These approximations are not bad as long as v/c 0.1

10 Nuclear Binding Energies (What drives stability) 1. General Definition : ass is converted into potential energy which holds the system together. Consequence for relative motions of particles in nucleus (Note that nucleons in nucleus are in constant motion.) Examples (nucleus) < (Zp + Nn) (atom) < ((nucleus) + Ze) (molecule) < Σ (atoms) The difference in mass is what we call the BINDING ENERGY. (E=mc )

11 . Total Binding Energy: TBE TBE is the mass converted into energy when a nucleus is formed from its constituent nucleons and electrons. A Z X TBE c Z 1 H + N 1 n + ; mass balance; LHS in u TBE ( A Z + N ( X )) c = ; energy balance; LHS in ev H n Z Substituting = A + Δ/c, TBE A = Z + N ( X ) ; analogous to the heat of condensation H n Z Reversing the equation defines nuclear vaporization TBE for the deuteron is. ev TBE for 38 U is ~ 000 ev

12 3. Average Binding Energy : <BE> BE = TBE A ; this quantity is more instructive the TBE. It is analogous to the molar heat of condensation rather than the heat involved in condensing an arbitrary amount. Example: 1 C 6 1 H n 1 C + TBE/c TBE = 6(7.89) + 6(8.071) 0 = ev BE = 9.160/1 BE = ev

13 4. Systematics of Average Binding Energies NOTE : LARGE <BE> IPLIES HIGH STABILITY i.e. particles bound tightly together <BE> 56 F e Fission Fusion A Note not zero on y-axis! 4 is very tightly bound!

14 KEY POINTS To first approximation <BE>~ 8 ev i.e. relatively constant, acts like a nonpolar liquid N Z 56 Fe most stable nucleus in nature Light nuclei -- <BE> increases with increasing A Therefore ENERGY RELEASED DURING FUSION (Stellar Energy) Fusion is the amalgamation of two nuclei to form a heavier nucleus. avy nuclei -- <BE> decreases with increasing A ENERGY IS RELEASED DURING FISSION (Nuclear Reactors) FISSION is the splitting of a heavy nucleus into two lighter nuclei. Fine structure Peaks quantum effects- shell structure Odd-even variations pairing effects

15 Nuclear Energetics 1. Particle Binding Energies B i Definition: The energy required to remove a particle from a nucleus (cf binding energy for e s in atoms). Cases: In principle, either a nucleon or cluster of nucleons can be removed a. Proton Binding Energy (or Separation energy) -- B p (or S p = - B p ) EQUATION: A Z X + B c p A 1 1 Z 1Y + 1 H CALCULATION: ( Y ) ( H ) ( X ) B p = +

16 b. Neutron Binding Energy B n (or S n = - B n ) EQUATION: A Z X + Bn A 1 Z X + c 1 0 n CALCULATION: B n = ( A 1 X ) + ( n) ( A X ) c. Alpha Particle ( 4 ) Binding Energy B α EQUATION: A Z X + Bα A 4 Z Y + c 4 CALCULATION: B α = (Y) + (α) (X) d. etc. Could do same for H, 1 C, 16 O

17 e. Example: Calculate B n for 1 Be 1 Be + B n 4 11 Be + 1 n 0 B n = ( 11 Be) + (n) ( 1 Be) ass Table (Nuclear Wallet cards) B n = ( ) ev B n = ev This means that if we supply ev to the 1 Be nucleus it will release a neutron.

18 3. Nuclear Reaction Energetics Q values Definition: Q is the energy RELEASED in a nuclear reaction, i.e. when two nuclei collide. i.e., for A + B C + D + Q Q = ( reac tan ts) ( products) SIGN of Q Q = + Q = - EXOTHERIC ENDOTHERIC NOTE: A negative Q value can always be overcome by accelerating one of the reactants and converting kinetic energy to mass energy.

19 b. Example: Fusion power utilizes the following reaction H + 3 H n + Q Q = ( H) + ( 3 H) ( 1 n) ( 4 ) Q = Q = ev Is this reaction exothermic or endothermic? This energy appears as the kinetic energy of both 4 and neutron and can be converted to heat.

20 Nuclear Decays (an introduction) see for example Ehmann and Vance Ch. Alpha Decay General form: A Z E A Z 4 4 F+ + ( γ ) Example: ( ) 84 Po 8Pb+ + γ Half-life (t 1/ ) of 10 Po is 138.4d. What is the Q value of this reaction? Q= ( 10 Po)- ( 06 Pb)- ( 4 ) Q= ( (.45)) = ev Where does this energy go?

21 Pb P P = Pb Pb V V = Pb Pb V V = = + Pb Pb V V Substituting, = + Pb Pb V V Rearranging, = + Pb V V

22 KE( )(1 + ) = KE( ) = 1+ Pb The actual decay energy observed for the alpha particle is ev. In addition to the case where the parent nucleus decays to the ground state of the daughter, it is also possible for the parent nucleus to decay to an excited state of the daughter nucleus. Consider a general case, KE( ) = ev Notice that in this generalized example, the parent nucleus E decays to the ground state of the daughter F, as well as its first and second excited state. The probability of each transition is called the branching ratio and is displayed in parentheses. As a result of this decay one would observe:

Radioactivity, Radiation and the Structure of the atom

Radioactivity, Radiation and the Structure of the atom What do you know (or can we deduce) about radioactivity from what you have learned in the course so far? How can we learn about whether radioactive