Introduc)on to Nuclear Physics Physics 110: Energy Physics 120: Energy and Technology R.L. Cooper 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 1 Atomic and Nuclear Structure •  Ice has well-­‐known macroscopic proper)es •  Apparent crystal structure •  What do we see when we examine closer? 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 2 Atomic and Nuclear Structure •  Molecules arrange themselves into a crystalline paMern •  Chemistry tells us water molecules are “composite” •  Can we look closer at structure? 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 3 Atomic and Nuclear Structure •  Water molecule is 2 hydrogen atoms and 1 oxygen atom •  What is the cause for the binding? •  Where do well-­‐ known “electrical” proper)es come? 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 4 Atomic and Nuclear Structure •  Nuclear scaMering tells us nega)ve electrons surround hard, posi)ve core •  Nucleus contains nearly all mass •  BB on football field for scale 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 5 Atomic and Nuclear Structure •  Nucleus contains posi)ve protons and nega)ve neutrons •  Nucleus has net posi)ve charge and aMracts electrons •  Strong force holds nucleus together 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 6 Chemistry and Periodic Table •  Chemistry is en)rely dictated by electrons •  Atom has same # of electrons as protons •  Neutrons can vary •  For small atoms # neutrons ≈ # protons Figure 13-5 p419
12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 7 Chemistry and Periodic Table 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 8 Clicker Ques)on #1 a) •  What is the energy “spectrum” that you expect for the electrons in a typical atom? b) a) Con)nuous b) Discrete – low-­‐energy c) Discrete – ladder-­‐like 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper Energy
Energy
c) Energy
9 Clicker Ques)on #1 a) •  What is the energy “spectrum” that you expect for the electrons in a typical atom? b) a) Con)nuous b) Discrete – low-­‐energy c) Discrete – ladder-­‐like 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper Energy
Energy
c) Energy
10 Discussion for Ques)on #1 •  Quantum mechanics tells us energy levels are “discre)zed” in increasing steps Figure 13-6 p420
12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 11 Clicker Ques)on #2 •  What is the main reason that the atomic mass is NOT close to an integer? (i.e. it has a decimal) a) neutron mass ≠ proton mass b) number of neutrons varies c) binding energy 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 12 Clicker Ques)on #2 •  What is the main reason that the atomic mass is NOT close to an integer? (i.e. it has a decimal) a) neutron mass ≠ proton mass b) number of neutrons varies c) binding energy 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 13 Discussion for Ques)on #2 •  mn = 1.0073 and mp = 1.0087 – masses contribute, but isotopes are biggest effect •  # neutrons ≈ # protons, BUT it can vary •  Chemistry unaffected, but nuclear physics can vary wildly Figure 13-8 p421
12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 14 Discussion for Ques)on #2 • 
24Mg occurs at 79% 25Mg occurs at 10% 26Mg occurs at 11% •  All stable / occur naturally •  We start to see # neutrons can be bigger than # protons •  Big atoms need more neutrons to reduce proton repulsion 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 15 Isotope Nota)on • 
A N
A
A
Z
X
or Z X
or X
X = chemical symbol  # protons (charge) A = atomic number = # neutrons + # protons Z = # protons  equivalent to X N = # neutrons = A -­‐ Z 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 16 Clicker Ques)on #3 •  How many neutrons are in the atom Magnesium-­‐25? a) 12 b) 25-­‐12 = 13 c) 25 d) 25+12 = 37 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 17 Clicker Ques)on #3 •  How many neutrons are in the atom Magnesium-­‐25? a) 12 b) 25-­‐12 = 13 c) 25 d) 25+12 = 37 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 18 Binding Energy •  Protons and neutrons (nucleons) “s)ck” together – need energy to separate p n p n 2mn + 2mp
=
4.032 amu 12/10/13 Figure 13-11 p426
•  Where did mass go? p n n p •  To binding energy •  Einstein E = mc2
mα = 4.0015 amu ∆m = 0.0305 amu Physics 110/120 -­‐-­‐ R.L. Cooper •  c = speed of light = 3 × 108 m / s 19 Binding Energy – A Calcula)on p n p n 2mn + 2mp
=
4.032 amu p n n p c
=
1 amu
=
3.0 × 108 m/s
1.66 × 10−27 kg
mα = 4.0015 amu ∆m = 0.0305 amu 0.0305 amu → 5.06 × 10−29 kg
E = mc2 = (5.06 × 10−29 kg)(3.0 × 108 m/s)2 = 4.6 × 10−12 J
•  Doesn’t seem like a lot, but consider the fusion to create 4 g •  4 g = 6.02 × 1023 molecules •  Total energy 2.8 × 1012 J  about 100 tons of coal! 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 20 Nuclear Reac)ons •  Nuclei can decay or be put together to manipulate energy and mass •  There are conserved quan))es –  mass (energy), mass number (A = N + Z), charge –  Examples: 42 He +147 N →178 O +11 H
•  A conserved (4+14 = 17+1), Z conserved (2+7 = 8+1) 238
92 U
4
→234
Th
+
90
2 He
•  A conserved (238 = 234+4), Z conserved (92 = 90+2) 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 21 Clicker Ques)on #4 •  Complete the fission reac)on. What is A, Z? 135
A
n +235
U
→
I
+
92
53
Z Y + 2n
a) 100, 39 b) 99, 39 c) 100, 38 d) 99, 38 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 22 Clicker Ques)on #4 •  Complete the fission reac)on. What is A, Z? 135
A
n +235
U
→
I
+
92
53
Z Y + 2n
a) 100, 39 b) 99, 39 c) 100, 38 d) 99, 38 12/10/13 HINT: n
Physics 110/120 -­‐-­‐ R.L. Cooper 1
→0
n
23 Clicker Ques)on #4 •  Complete the fission reac)on. What is A, Z? 135
A
n +235
U
→
I
+
92
53
Z Y + 2n
a) 100, 39 b) 99, 39 c) 100, 38 d) 99, 38 12/10/13 HINT: n
Physics 110/120 -­‐-­‐ R.L. Cooper 1
→0
n
24 Discussion for Ques)on #4 n
1
0n
235
+ 92
U
135
→ 53
I
A
+Z
Y + 2n
135
A
2
+235
U
→
I
+
Y
+
92
53
Z
0n
•  Superscript A: 1+235 = 135+A+2  A = 99 Subscript Z: 92 = 53 + Z  Z = 39 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 25 Radioac)vity •  Some isotopes are NOT stable, and will decay Table 13-1 p423
Figure 13-9 p423
12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 26 Decay Rates •  τ 1/2
is half-­‐life N (t) = N (0)2−t/τ1/2
•  Equivalent to exponen)al decay N (t) = N (0)e
Figure 13-10 p424
−t/T
•  where τ1/2 = ln (2) T = 0.69 T
12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 27 Clicker Ques)on #5 •  At 9:00 am on Monday, a radioac)ve sample contained 4 million nuclei. At 9:00 am on Friday, 3 million had decayed. What is the half-­‐life? a) 5 days b) 4 days c) 3 days d) 2 days e) 1 day 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 28 Clicker Ques)on #5 •  At 9:00 am on Monday, a radioac)ve sample contained 4 million nuclei. At 9:00 am on Friday, 3 million had decayed. What is the half-­‐life? a) 5 days b) 4 days c) 3 days d) 2 days e) 1 day 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 29 Discussion for Ques)on #5 •  Started with 4 million, now have 4 – 3 million = 1 million •  We have ¼ of the original amount  2 half-­‐lives (½, ¼, ⅛, …) – frac)on (1, 2, 3, …) – half-­‐lives •  Total )me was 4 days •  4 days / 2 half-­‐lives = 2 days / 1 half-­‐life 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 30 Clicker Ques)on #6 •  Sample A has 2 million Co-­‐60 atoms and Sample B has 1 million Co-­‐60 atoms. The decay rate of Sample A is what rela)ve to Sample B? What is the life)me? a) ×2 rate, same life)me b) same rate, same life)me c) ×2 rate , ×2 life)me d) same rate, ×2 life)me 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 31 Clicker Ques)on #6 •  Sample A has 2 million Co-­‐60 atoms and Sample B has 1 million Co-­‐60 atoms. The decay rate of Sample A is what rela)ve to Sample B? What is the life)me? a) ×2 rate, same life)me b) same rate, same life)me c) ×2 rate , ×2 life)me d) same rate, ×2 life)me 12/10/13 Physics 110/120 -­‐-­‐ R.L. Cooper 32 Discussion for Ques)on #6 •  The life)me is an intrinsic proper)es of an unstable atom – changing the number does not change its decay rate •  The instantaneous rate is propor)onal to the exis)ng number N (t) = N (0)e
12/10/13 −t/T
Physics 110/120 -­‐-­‐ R.L. Cooper 33