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Constants and Formulas

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HKDSE Physics 物理
Constants and Formulas 常數與公式
(Compulsory + E2E3 必修 + E2E3)
Constants 常數:
A. Heat and Gases 熱和氣體
i.
𝑐 = 4200 Jkg −1 °C −1
Specific Heat Capacity of Water
水的比熱容量
ii.
𝑙f = 3.34 × 105 Jkg −1
Specific Latent Heat of Ice
冰的熔解比潛熱
iii.
𝑙v = 2.26 × 106 Jkg −1
Specific Latent Heat of Vapour
水的汽化比潛熱
iv.
𝑅 = 8.31 mol−1 K −1
Universal Gas Constant
普適氣體常數
v.
𝑁𝐴 = 6.0221 × 1023 mol−1
Avogadro Constant
阿弗加德羅常數
B. Force and Motion 力和運動
i.
𝑔 = 9.81 ms −1
Acceleration of Gravity
重力加速度
ii.
𝐺 = 6.67 × 10−11 m3 kg −1 s −2
Gravitational Constant
萬有引力常數
Constants and Formulas
1
C. Wave Motion 波動
i.
𝑐0 = 3.00 × 10−1
Speed of Light
光速
D. Electricity and Magnetism 電和磁
i.
𝜀0 = 8.85 × 10−12 A2 s 4 m−3 kg −1
Permitivity of Vacuum
真空電容率
ii.
𝜇0 = 1.26 × 10−6 TmA−1
Permeability of Vacuum
真空磁導率
E. Radioactivity and Nuclear Energy 放射現象和核能
i.
𝑒 = 1.60 × 10−19 C
Charge of Electron
電子電荷
ii.
𝑢 = 1.6605 × 10−27 kg
Atomic Mass Unit
原子質量單位
F. Atomic World 原子世界
i.
ℎ = 6.63 × 10−34 𝑚2 𝑘𝑔𝑠 −1
Planck Constant
普朗克常數
G. Energy and Use of Energy 能量和能源的使用
i.
𝑆 = 1366 𝑊𝑚−2
Solar Constant
太陽常數
Constants and Formulas
2
Formulas 公式:
A. Heat and Gases 熱和氣體
A1. Internal Energy 內能
i.
𝐶 = 𝑚𝑐
Heat Capacity
熱容量
ii.
𝑄 = 𝑚𝑐𝛥𝑇
Energy with Change of Temperature
溫度改變時的能量
iii.
𝑄 = 𝑚𝑙f = 𝑚𝑙v
Energy with Change of States
物態改變時的能量
iv.
𝑃=
𝐸
Power
𝑡
功率
A2. Gases 氣體*
v.
𝐹
𝑝=𝐴
Pressure
壓強
vi.
Boyle’s Law
𝑝1 𝑉1 = 𝑝2 𝑉2 = 𝑘
波義耳定律
vii.
𝑝1
𝑇1
=
𝑝2
𝑇2
=𝑘
Pressure Law
氣壓定律
viii.
𝑉1
𝑇1
𝑉
= 𝑇2 = 𝑘
Charle’s Law
2
查理定律
ix.
𝑝𝑉 = 𝑛𝑅𝑇
𝑝1 𝑉1
𝑛1 𝑇1
Universal Gas Law
𝑝 𝑉
= 𝑛2 𝑉2
普適氣體定律
2 2
Constants and Formulas
3
x.
𝑚
𝜌=
Density
𝑉
密度
xi.
4
𝑉sphere = 3 𝜋𝑟 3
Volume of a Sphere
球體體積
xii.
𝑛=
𝑚
Molar Number
𝑀
摩爾數
1
xiii. 𝑝𝑉 = 3 𝑁𝑚𝑐̅̅̅2
Kinetic Equation of Gases
氣體分子運動方程
xiv.
3
3𝑅𝑇
1
𝐸K = 2 𝑛𝑅𝑇 = 2𝑁 = 2 𝑁𝑚𝑐̅̅̅2
Kinetic Energy of Molecules
𝐴
氣體分子動能
xv.
3𝑝𝑉
2𝐸
√̅̅̅
𝑐 2 = √ 𝑁𝑚 = √ 𝑁𝑚K
R.M.S. of Velocity of Molecules
氣體分子的方均根速率
B. Force and Motion 力和運動
B1. Movement 移動
i.
𝑠
𝑣 = = 𝑟𝜔
Velocity
𝑡
速度
ii.
𝑎=
𝑣
Acceleration
𝑡
加速度
iii.
𝑣 = 𝑢 + 𝑎𝑡
Equations of Uniform Accelerating
1
𝑠 = 𝑢𝑡 + 2 𝑎𝑡 2
Motion
𝑣 2 = 𝑢2 + 2𝑎𝑠
勻速直線運動方程
Constants and Formulas
4
B2. Force 力
iv.
Newton’s Second Law of Motion
𝐹 = 𝑚𝑎
牛頓第二運動定律
v.
𝑊 = 𝑚𝑔
Weight
重量
vi.
𝜏 = 𝐹 × 𝑑sin𝜃
Moment of a Force
力矩
B3. Energy and Momentum 能量與動量
vii.
𝑊 = 𝐹𝑠cos𝜃
Work
功
1
viii. 𝐸K = 2 𝑚𝑣 2
Kinetic Energy in Mechanics
機械動能
ix.
𝐸P = 𝑚𝑔ℎ
Potential Energy of Gravity
重力勢能
x.
𝑃 = 𝐹𝑣
Power in Mechanics
機械功率
xi.
𝑝 = 𝑚𝑣
Momentum
動量
xii.
𝑚1 𝑢1 + 𝑚2 𝑢2 = 𝑚1 𝑣1 + 𝑚2 𝑣2
Conservation of Momentum
動量守恆式
xiii.
1
2
1
𝑚1 𝑢12 + 𝑚2 𝑢22
Conservation of Kinetic Energy
2
1
1
= 2 𝑚1 𝑣12 + 2 𝑚2 𝑣22
動能守恆式
B4. Circular Motion 圓周運動*
xiv.
𝜔=
𝜃
Angular Velocity
𝑡
角速度
Constants and Formulas
5
xv.
𝑇=
2𝜋
Period of Circular Motion
𝜔
圓周運動的週期
xvi.
𝑎 = 𝑟𝜔2 =
𝑣2
Centripetal Acceleration
𝑟
向心加速度
xvii. 𝐹 =
𝑚𝑣 2
𝑟
= 𝑚𝑟𝜔2
Centripetal Force
向心力
B5. Gravitation 引力*
xviii. 𝐹 =
𝐺𝑚1 𝑚2
Law of Universal Gravitation
𝑟2
萬有引力定律
xix.
𝑔=
𝐺𝑀E
2
𝑅E
𝐹
=𝑚
Gravitational Field Strength
引力場強度
xx.
xxi.
𝐺𝑀 = 𝑟 3 𝜔2 = 𝑣 2 𝑟
Gravitation and Circular Motion
𝐺𝑀𝑇 2 = 4𝜋 2 𝑟 3
引力和圓周運動
𝐺𝑀
𝑣=√
Orbital Velocity
𝑟
軌道速度
𝑟3
xxii. 𝑇 = 2𝜋 √𝐺𝑀
Orbital Period
軌道週期
C. Wave Motion 波動
C1. Refraction 折射
i.
𝑛=
sin𝑖
Refractive Index
sin𝑟
折射率
Constants and Formulas
6
ii.
Snell’s Law
𝑛1 sin𝜃1 = 𝑛2 sin𝜃2
斯涅耳定律
iii.
n
𝑐 = sin−1 (n1 )
Critical Angle
2
臨界角
C2. Lenses 透鏡
iv.
ℎo
ℎi
𝑑
= 𝑑o
Magnifying Rate of Lens
i
透鏡放大率
v.
1
1
1
+𝑣 =𝑓
𝑢
Formula of Single Lens*
單塊透鏡公式*
C3. Phenomena of Waves 波的現象
vi.
𝑣 = 𝑓𝜆
Speed of Waves
波速
vii.
1
𝜆∝𝑛∝𝜃∝𝑣
Relationship of Transverse Wave
橫波關係式
viii. 𝛥𝑦 =
𝜆𝐷
Double Slits Experiment*
𝑎
雙縫實驗*
ix.
𝑑sin𝜃 = 𝑛𝜆
Grating*
光柵*
D. Electricity and Magnetism 電和磁
D1. Electrostatic 靜電學
i.
𝐹=
𝑄1 𝑄2
Coulomb’s Law
4𝜋𝜀0 𝑟 2
庫倫定律
Constants and Formulas
7
ii.
𝑄
𝐹
𝐸 = 4𝜋𝜀
2
0𝑟
=𝑞
Electric field Strength
電場強度
iii.
𝑉
𝐸=𝑑
Electric field Strength in Parallel
Plate
平行板的電場強度
D2. Circuit 電路
iv.
𝑄
𝐼=
Current
𝑡
電流
v.
𝑉=
𝐸
Voltage
𝑞
電壓
vi.
Ohm’s Law
𝑉 = 𝐼𝑅
歐姆定律
vii.
𝑅=
𝜌𝑙
Resistance of a Wire
𝐴
導線電阻
viii. 𝑅eq = 𝑅1 + 𝑅2
Equivalent Resistance of Series
Circuit
串聯電路的等效電阻
ix.
1
𝑅eq
=
1
𝑅1
+
1
Equivalent Resistance in Parallel
𝑅2
Circuit
並聯電路的等效電阻
x.
𝜀 = 𝑉 + 𝐼𝑟
Internal Resistance
內阻
xi.
𝑃 = 𝑉𝐼 = 𝐼 2 𝑅 =
𝑉2
Electrical Power
𝑅
電功率
Constants and Formulas
8
xii.
𝐸 = 𝑃𝑡 = 𝑉𝐼𝑡 = 𝐼 2 𝑅𝑡 =
𝑉2 𝑡
Electrical Energy
𝑅
電能
D3. Electromagnetism 電磁學
𝜇 𝐼
0
xiii. 𝐵 = 2𝜋𝑟
Magnetic Field of a Long Straight
Wire
長直導線的磁場
xiv.
𝐵=
𝜇0 𝑁𝐼
𝑙
= 𝜇0 𝑛𝐼
Magnetic Field of a solenoid
螺線管中的磁場
xv.
𝐹 = 𝐵𝐼𝑙sin𝜃
Magnetic Force
磁力
xvi.
𝜏 = 𝑁𝐵𝐴𝐼
Torque of Coil in a Motor
電動機中線圈的轉矩
xvii. 𝐹 = 𝐵𝑄𝑣sin𝜃
Force of a Charge inside Magnetic
Field
電荷在磁場內的磁力
xviii. 𝜁 = −
𝑁𝛥𝛷
Faraday’s Law
𝛥𝑡
法拉第定律
xix.
𝜁 = 𝐵𝑙𝑣
Induced e.m.f. of Wire Cutting
Magnetic Field
導線切割磁場的感生電動勢
D4. Transformer 變壓器*
xx.
√𝐼̅2 = 𝐼max
2
R.M.S. of Current
√
電流的方均根值
Constants and Formulas
9
xxi.
𝑉
√̅̅̅̅
𝑉 2 = max
R.M.S. of Voltage
√2
電壓的方均根值
xxii.
𝑁P
𝑁S
𝑉
𝐼
≈ 𝑉P ≈ 𝐼S
S
Ratio of Principle Coil and
P
Supplementary Coil
原線圈與副線圈之比
E. Radioactivity and Nuclear Energy 放射現象和核能
E1. Radioactive Decay 放射衰變*
i.
𝐴 = 𝑘𝑁
Activity and Number of Undecayed
Nuclei
放射強度與未衰變原子核數目
ii.
1 𝑛
𝐴 = 𝐴0 𝑒 −𝑘𝑡 = 𝐴0 (2)
Activity
放射強度
iii.
1 𝑛
𝑁 = 𝑁0 𝑒 −𝑘𝑡 = 𝑁0 (2)
Exponential Equation of Decay
衰變指數方程
iv.
𝑡1 =
2
ln2
Half Time
𝑘
半衰期
v.
𝑁 = 𝑛𝑁𝐴
Number of Nuclei and Molar
Number
原子核數目和摩爾數
E2. Nuclear Energy 核能*
vi.
𝛥𝐸 = 𝛥𝑚𝑐 2
Mass-energy Relationship
質能關係式
Constants and Formulas
10
vii.
𝑃 = 𝐴𝐸 = 𝑘𝑁𝐸
Power of Nuclear Energy
核能功率
F. Atomic World 原子世界
F1. Photoelectric Effect 光電效應
i.
𝐾𝐸max = 𝑒𝑉𝑠
Maximum Kinetic Energy with
Stopping Potential
最大動能與遏止電勢
ii.
𝐸 = ℎ𝑓
Energy of a Photon
光子能量
iii.
Albert Einstein’s Photoelectric
𝐾𝐸max = ℎ𝑓 − 𝜑
Equation
愛恩斯坦光電方程
iv.
ℎ
𝑉𝑠 = 𝑒 𝑓 −
𝜑
Relation of Stopping Potential and
𝑒
Frequency
遏止電勢與頻率的關係
F2. Transition of Hydrogen Atom 氫原子的激發
v.
𝐸=−
13.6𝑒𝑉
Energy Level of a Hydrogen Atom
𝑛2
氫原子的能階
vi.
𝐸𝑎→𝑏 = 𝐸𝑏 − 𝐸𝑎
Energy Level Difference
能階差
vii.
1
=−
𝜆
13.6𝑒
ℎ𝑐
1
1
(𝑎2 − 𝑏2 )
Required Wavelength for Transition
激發的所需波長
Constants and Formulas
11
F3. Nanotechnology 納米技術
ℎ
ℎ
viii. 𝜆 = 𝑝 = 𝑚𝑣
De Brogile Formula
德布羅意公式
ix.
𝜃≈
1.22𝜆
Rayleigh Criterion
𝑑
瑞利判據
x.
𝑠 = 𝑟𝜃
Smallest Linear Length
最小線性長度
xi.
𝜆=
ℎ
Wavelength of TEM
√2𝑚𝑒𝑉
透射電子顯微鏡的波長
G. Energy and Use of Energy 能量和能源的使用
G1. Domestic Electricity 家居用電
i.
𝜂=
𝑃𝑜𝑢𝑡
Efficiency
𝑃𝑖𝑛
效率
ii.
𝛷
Lighting Efficiency = 𝑃
Lighting Efficiency
𝑖𝑛
發光效率
iii.
𝛷
𝐸 = 4𝜋𝑟 2 cos𝜃
Illumination
照明度
iv.
Cooling Capacity =
𝑄𝐶
Cooling Capacity
𝑡
製冷量
v.
𝐶𝑂𝑃 =
Cooling Capacity
Coefficient of Performance
𝑃𝑖𝑛
性能係數
Constants and Formulas
12
vi.
𝑄𝐻 = 𝑄𝐶 + 𝑊
Energy Conversion in Air
Conditioning
冷氣的能量轉換
G2. Energy Use in Architecture 建築上的能量使用
vii.
𝑈=
𝜅
U-value
𝑑
U值
viii. 𝑃 = 𝑈𝐴𝛥𝑇
Power of Transfering Heat
熱傳導係數
ix.
𝑃
OTTV = 𝐴
Overall Thermal Transfer Value
總熱傳送值
G3. Energy Sources 能源
x.
𝐸 = |𝑚𝑝 + 𝑚𝑛 − 𝑚|
Combined Energy
結合能
xi.
1
𝑃 = 2 𝜂𝜌𝐴𝑣 3
Power of Wind Turbine
風力渦輪機的功率
xii.
𝑃 = 𝑆𝐴𝜂cos𝜃
Power of Solar Panel
太陽能板的功率
Remarks 備註:
有 * 標示的為延展部分課程。
Those marked with * are extended syllabuses.
Constants and Formulas
13
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