I.3 守恆原理
 I.3.1 能量守恆
 I.3.2 動量守恆
 I.3.3 角動量守恆
I.3.1 能量守恆
 一個隔絕系統內的能量，可以在動能，
位能，熱能甚至質量之間互相轉換，但
該系統之總能量維持不變。
 K (動能) = 1/2 mv2
 U (位能) = mgh
重力位能
= 1/2 kx2
彈性位能
Ex. 3-1 木塊-彈簧系統
Ex. 3-2 單擺
I.3.2 質能互換
 E = mc2
 Q = mc2
– Q：反應中所釋放或吸收的能量
–  m：反應物在反應後增加或減少之質量
 化學反應
 核分裂反應
 核融合反應
Nuclear Binding Energy
Ex. 3-3 化學反應
2H2＋O2  2H2O
Q = 4.85×105 J
Q
4.8510 J
12
m  2 

5
.
39

10
kg
2
c
3.00108 m/s
5


反應物質量 M = 2(2.0g)＋32.0g = 0.036㎏
質量變化率:
m 5.391012 kg
f 

 1.6 1010
m
0.036kg
核分裂反應的發現
 德國物理學家 Otto Hahn 及 Fritz
Strassmann 在1939年研究輻射問題時所
發現
 中子 + 鈾235  氪 + 鋇 + 中子
A nuclear fission
Ex. 3-4 核分裂反應－ 鈾235
n  140Ce ＋ 94Zr ＋ 2n
鈾 中子 鈰
鋯
235.04U 1.00867U 139.91U 93.91U
反應前後之質量差 m
= ( 235.04＋1.00867 ) － (139.91＋93.91＋
2 ×1.00867 ) = 0.211u
釋放能量Q =  mc2= 0.211u ×932
= 197 Mev
235U＋
Ex. 3-4 Nuclear Fission
釋放能量Q = 197 Mev
（一般化學反應僅數個電子伏特）
m = 235.04u＋1.00867u = 236.65u
質量變化率f = m/m = 0.00089 ~ 0.1﹪
核融合反應
氘 + 氘  氦3 + 中子 + 能量
氘 + 氚  氦4 + 中子 + 能量
氘
氚
核
融
合
反
應
A nuclear fusion
Ex. 3-5 核融合反應－氘(重水)
D ＋ D  T ＋ p
氘
氚
質子
2.01410u 3.01605u 1.00783u
m = 2×2.01410－3.01605－1.00783
= 0.00432u
Ex. 3-5 Nuclear Fusion
Mev
Q  mc  0.00432u 932
u
 4.03Mev
2
m
0.00432
f 

 0.1 %
m
2  2.01410
I.3.3 核反應器(Nuclear Reactors)
 連鎖反應 (Chain Reactions)
–核彈
–核能電廠
 核反應器之基本結構
 恆星的融合反應(太陽)
 地球上試驗的融合反應
–磁圍阻
–慣性圍阻
連鎖反應 (Chain Reaction)
核彈
核能電廠
Chain Reactions
 核彈
– 實際上每次分裂釋出2.5個中子
(平均值)
 核能電廠
– 每次分裂釋出一個中子
• Critical (臨界)
• Subcritical (次臨界)
• Supercritical (超臨界)
Atomic Bomb, Hydrogen Bomb
and the Plutonium
 Ne: 2.3 days Pu: 24000y
 Both are 
原子彈
Hiroshima from the ground
Nagasaki after the Bomb
氫彈
Hell opens up
Ballistic missile submarine:
a threat to world peace
Submarine-launched ballistic
missile
核反應器之基本結構
 燃料棒－3﹪235U (0.07%)
 控制棒－B、Cd
 緩衝劑－水
Reactor Core
The Nuclear Fuel Cycle
Olympic Dam Pit Head
In-Situ Leach Mining
Radioactive Wastes
Depleted Uranium
The Pressurized Water Reactor (PWR)
The Boiling Water Reactor (BWR)
Ex. 3-6 壓水式反應器
300℃ + 150 atm
Nuclear Power Plant Accidents
 1952 Dec. 12, Chalk River, nr. Ottawa, Canada
 1957 Oct. 7, Windscale Pile No. 1, north of
Liverpool, England
 South Ural Mountains:
 1976 nr. Greifswald, East Germany
 1979 March 28, Three Mile Island, nr.
Harrisburg, Pa.
 1986 April 26, Chernobyl, nr. Kiev, Ukraine
 1999 Sept. 30, Tokaimura, Japan
Nuclear Power Plant Accidents
 1952 Dec. 12, Chalk River, nr. Ottawa, Canada:
a partial meltdown of the reactor's uranium fuel
core resulted after the accidental removal of four
control rods. Although millions of gallons of
radioactive water accumulated inside the reactor,
there were no injuries.
 1957 Oct. 7, Windscale Pile No. 1, north of
Liverpool, England: fire in a graphite-cooled
reactor spewed radiation over the countryside,
contaminating a 200-square-mile area.
Nuclear Power Plant Accidents
 South Ural Mountains: explosion of radioactive
wastes at Soviet nuclear weapons factory 12 mi
from city of Kyshtym forced the evacuation of
over 10,000 people from a contaminated area. No
casualties were reported by Soviet officials.
 1976 nr. Greifswald, East Germany:
radioactive core of reactor in the Lubmin nuclear
power plant nearly melted down due to the
failure of safety systems during a fire.
Nuclear Power Plant Accidents
 1979 March 28, Three Mile Island, nr.
Harrisburg, Pa.: one of two reactors lost
its coolant, which caused overheating and
partial meltdown of its uranium core. Some
radioactive water and gases were released.
Nuclear Power Plant Accidents
 1986 April 26, Chernobyl, nr. Kiev, Ukraine:
explosion and fire in the graphite core of one
of four reactors released radioactive material
that spread over part of the Soviet Union,
eastern Europe, Scandinavia, and later
western Europe. 31 claimed dead. Total
casualties are unknown. Worst such accident
to date.
Nuclear Power Plant Accidents
 1999 Sept. 30, Tokaimura, Japan:
uncontrolled chain reaction in a uraniumprocessing nuclear fuel plant spewed high
levels of radioactive gas into the air killing
one worker and seriously injuring two
others. Japan's worst nuclear accident.
太陽的融合反應
 太陽的輻射功率 = 3.9 ×1026 W
 如為化學反應，以太陽質量，僅能
維持1000年；如為重力收縮~107年，
但太陽的壽命已有50億年，不可能
是核分裂，因為沒那麼多鈾。
 結論: 融合反應（P-P cycle）
氘
氚
核
融
合
反
應
A nuclear fusion
P-P cycle － 1
點火溫度：一千五百萬度
氫
 氦
P-P cycle － 2
 氫燒完之後呢? 星球的演變
 恆星是製造重元素的工廠
 2個 (質子) 發生融合的機率~10-26，因此
不會如同氫彈般爆炸。但恆星內部的氫
密度極高，既使反應機率極低，仍可維
持穩定的融合反應。另一方面，此反應
之速率太慢，在地球上無法進行。
地球上試驗的融合反應
 D－T cycle ( 點火溫度：4千6百萬度)
 D－D cycle ( 點火溫度：4億度)
 全電荷產物反應 (不需熱交換，但點火
溫度更高)
Heat Cycle
D－T cycle
D ＋ T  4He ＋ n
n ＋ 6Li  4He ＋ T（氚）
D－D cycle
D＋D  T ＋P
D ＋ D  3He ＋ n
全電荷產物反應
D ＋ 3He  4He ＋ P
P ＋ 6Li  4He ＋ 3He
P ＋ 11B  3 4He
磁圍阻(Magnetic Confinement)
 在融合反應的高溫下，物質呈完全游離
狀態 ，即電漿(plasma)態，必須以巧妙
方式〝盛裝〞
電荷平行電場/磁場
電荷被加速
電荷不受影響
電荷垂直電場/磁場
電荷被偏向，
但可通過電場
電荷被偏向，
且無法通過磁場
線圈（螺絲管）的磁場
螺絲環（Toroid）的磁場
Tokamak
磁圍阻核融合反應器的磁場
電
漿
圍
阻
普林斯頓大學的TFTR
（Tokamak Fusion Test Reactor）
Plasma Heating
 Ohmic Heating
 Neutral-Beam Injection
 Magnetic Compression
 Radio-frequency Heating
Fusion Power Plant
新星核融合反應器
高以高功率（2 ×1014W）釹釔榴石雷射射
擊燃料粒（D-T混合物）誘發核融合
Fuel pellets
Progress in Magnetic Fusion Power
Comparison of Coal and Fusion
Power
The Advantage of Fusion
Energy
 Abundant Fuel Supply
 No Risk of a Nuclear Accident
 No Air Pollution
 No High-level Nuclear Waste
 No Generation of Weapons Material