Atomic World 微觀世界
Chapter 1 Photoelectric Effect
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這一個章節基本上都是背爲主，因此大家要準備好紙和筆！
Photoelectric effect 光電效應
光電效應（Photoelectric Effect）是一個物理現象，指的是當光照射到某些材料時，會產生電子的放射現象。這一現象首次被阿爾伯特·愛因斯坦解釋並解釋光的粒子性質，是量子力學的重要實驗之一，也是對光的特性研究的重要基礎。
必背答案 Classical wave theory Contradiction 1：No time delay
Classical wave theory prediction
Electrons in the metal need time to absorb enough energy before they can escape and this delay will be longer if the intensity is low
Photoelectric effect
It is a one-to-one relationship. An electron can be ejected instantaneously if it accepts a photon of energy larger than the of the metal/ If a single photon has sufficient energy to knock out an electron, the electron gains enough energy in just one collision
必背答案 Classical wave theory Contradiction 2：Range of KE
Classical wave theory prediction
The photoelectrons are emitted with a range of KE. Only those free electrons at the surface can possess the max KE It is independent to the intensity of light
Photoelectric effect
(KEmax should be higher when the radiation has a greater intensity gains enough energy in just one collision
必背答案 Classical wave theory Contradiction 3：Threshold frequency
Classical wave theory prediction
Threshold frequency (f0) is the minimum value of frequency which can trigger the Photoelectric Effect
Work function (Φ) =hf0 is the minimum energy required to eject an electron Different metals have different values of Φ
Photoelectric effect
The emission of photoelectrons should occur at any frequency, provided that the incident radiation has enough intensity
必背答案 Classical wave theory Agreement：Threshold frequency
Classical wave theory prediction
Intensity of light no. photoelectrons
Photoelectric effect
rate of emission increases with intensity
The quantum theory of light：Photons
A beam of light is actually a stream of light quanta, called photons.
Energy of a photon
Energy E of each photon is proportional to the frequency f of the light
$$E=hf$$
$$h\text{ is the Planck constant}=6.63\times10^{-34}\text{ J s}$$
Wave-particle duality 波粒二象性
light
wave: diffraction, interference
particle: Photoelectric effect
Relationship among intensity no. of photons frequency
$$I(intensity)\propto nf\\n\propto\frac1f$$
- 提升intensity，有更多photons
- 相同intensity，提升photons，frequency下降
- 相同intensity，提升frequency，photons數量下降
Einstein’s photoelectric equation
Photoelectric equation
$$\mathrm{eV_s=hf-hf_0}$$
$$\frac12\mathrm{mv_{max}}^2=\mathrm{KE}_{\mathrm{max}}=\mathrm{hf}-\phi $$
Be careful!!!
- The unit of hf is J
- The unit of eVs is eV
- 𝟏𝒆𝑽 = 𝟏.𝟔×𝟏𝟎-𝟏𝟗𝑱
Stopping Potential
stopping potental的意思就是要額外給與多少potential difference 才能令到KE最大的electron也過不去對面的circuit
Chapter 2 Atomic Models and Spectra
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老實説，這一課真的很多理論要背！
Thomson’s plum pudding model
An atom was a large positively charged sphere with negatively charged electrons placed all over it
Alpha particle scattering experiment
They shot a beam of fast-moving α particles at a piece of thin gold foil, and observed how they were deflected
Experiment results
A relation between the number of α particles detected N and the deflection angle ϕ was obtained
必背：Experiment findings
- Most of them passed through the gold foil with very little or no deflections
- Some deflected at
large angles - A few bounced back
Thomson’s model could not explain why the α particles are bounced back
The electric force from a large +ve charged sphere would not be large enough to bounce the α particles back
Rutherford’s atomic model
必背：model details
- most of the volume of an atom is empty space
- electrons orbit around the nucleus in circular orbits
- positive charge and almost all the mass are concentrated in the small nucleus at the centre
explain α particle scattering experiment
| Experimental observation | Explanation |
| Most of the α particles pass through the gold foil with very little or no deflections | Most of the volume of an atom is empty space |
a strong repulsive electric force is exerted on any α particle coming close and deflects it only a few α particles bounce back or deflect at large angles | All the positive charge and almost all the mass of an atom are concentrated in the small nucleus at the centre |
Limitations of Rutherford’s atomic model
Failure to explain the atomic stability
- An electron orbiting around the nucleus is accelerating
- According to the electromagnetic theory, a charged particle emits EM radiation when it accelerates. It will lose energy continuously
If electron keeps losing energy by emitting EM radiation, it would spiral into the nucleus, collapsing the atom
Failure to explain the atomic line spectra
- When a low-pressure gas is heated, it emits light of some characteristic wavelengths, as shown by the discrete lines in its spectrum
- These lines are produced by individual atoms. Such a spectrum is called an atomic spectrum
- It implies that atoms only emit discrete amounts of energy in the form of photons
- However, electrons in Rutherford atoms can move in an orbit of any radius
- The gas is expected to release energy of any value, i.e. emit light with a continuous range of wavelength
Importance of scattering experiments
By performing scattering experiments, scientists are able to study more about the structure of an atom and to search for new particles
簡單而言，就是不斷撞，撞到分裂爲止。如果分裂到就即是說有更細的組成單位。
例如：
- Experiments revealed that the nucleus actually consists of two types of subatomic particles: protons and neutrons
- Later researches confirmed that they are made up of even smaller particles called quarks
Atomic spectra：Continuous spectrum
- When heated, solids, liquids and high-pressure gases emit light with a continuous range of wavelengths
- If we split the light with a prism or a plane transmission grating, we get a continuous spectrum
Atomic spectra：Emission line spectra
- low-pressure gases, when heated, emit light of some characteristic wavelengths only
- Each of their spectra shows a set of discrete lines.
- We call such a spectrum a line spectrum and the lines the spectral lines
- Since the spectrum is formed when the atoms in the gas emit light, it is specifically called an emission spectrum
- The bright spectral lines are called emission lines
Atomic spectra：Absorption line spectrum
- When we let light with a continuous range of wavelengths pass through a cooler low-pressure gas, we get a continuous spectrum with dark lines
- Formation of the dark lines shows the atoms in the gas only absorb photons of some characteristic wavelengths
- This kind of spectrum is called an absorption spectrum
順帶一提，將absorption spectrum與emission spectrum結合就是continuous spectrum
Energy levels of an atom
- The energy of an EM radiation is absorbed and emitted in discrete packets called photons
- Since an atom can only absorb and emit photons of certain specific wavelengths
- ⇒ the energy of an atom can only take on certain allowable energy values, known as the atomic energy levels
- When an atom loses energy by emitting a photon, it can only jump to a certain lower energy level
Emitting photons
如果electron要loss energy發出photon，electron就只能掉落在已既定的energ level上
Absorbing photons
同樣道理，如果electron要absrob energy from photo你，electron就只能跳上去已既定的energy level上
一會兒會再回來 absorbing photons 這個現象上
Bohr’s model of the hydrogen atom
Bohr modified Rutherford’s atomic model that successfully explained line spectra
必背：Postulates of Bohr’s atomic model
Postulate 1: Validity of Rutherford’s model
- Electron orbits around the nucleus in a circular path (from Rutherford’s model)
- The centripetal force for the motion is provided by the attractive electric force from the nucleus (from Rutherford’s model)
Postulate 2: Stationary orbit and quantized energy
- Electron orbits around the nucleus in certain allowed orbits without emitting EM radiation
- These orbits are called stationary orbits
- An atom with its electron moving in a stationary orbit is in a stationary state
Postulate 3: Atomic transition
- An atom can only emit or absorb a photon when it jumps from one energy level to another, i.e. the orbiting electron jumps from one stationary orbit to another
- Such a jump is called a transition
The energy of the emitted or absorbed photon must be equal to the energy difference between the energy levels:
$$\Delta E=E_\text{higher}-E_\text{lower}=hf$$
Since only photons of some characteristic wavelengths (energy values) can be emitted or absorbed, this explains why emission and absorption lines are formed
Postulate 4: Quantized angular momentum
Bohr introduced the quantum condition to determine the stationary orbits:
$$\begin{aligned}\text{The angular momentum of the electron can only be}\\\text{integral multiples of }\frac h{2\pi}\text{(i.e. quantized)}\end{aligned}$$
$$m_e\nu r=n\frac h{2\pi}\quad\mathrm{~for~}n=1,2,3…$$
常問問題：why do photons emit only in several wavelengths
必背答案
When an atom transits from a higher level to a lower one, photon with energy equals to the energy difference between the level is emitted.
Since energy levels ae quantized, the energy and thus wavelength of the photons emitted can only take some discrete values only
常問問題：Why does the atom not absorb the photon?
必背答案
The energy carried by photon does not match the difference of any two energy levels.
常問問題：Bohr's model classical aspect
必背答案
- Electrons are considered to be a particle revolving around the nucleus in definite orbits circular motion.
- The centripetal force is provided by the coulomb force between the protons and the electrons.
- The motion of electron obeys Newton’s law of motion.
Energy levels of the hydrogen atom
r1 = is the radius of the innermost orbit (at the n = 1 state), called the Bohr radius.
n = 1 state is ground state which is the most stable state.
$$E_n=-\frac{13.6\text{ eV}}{n^2}\quad\mathrm{for~}n=1,2,3…$$
All other states with n > 1 : excited states
- n = 2 = 1st excited state
- n = 3 2nd excited state
常問問題：爲何能量值是負數
必背答案
negative sign indicates that:
- electron is bound to the atom or
- the force between the nucleus and electron is attractive or
- work has to be done to move the electron to infinity
Energy level diagram
- All the energy levels of the stationary states are negative, i.e. the electron is bound by the attractive electric force from the nucleus
- The lower the level, the more negative is the energy
- Energy is required to pull the electron away from the nucleus
- The higher energy levels are packed closer together
The energy required to raise an atom from a lower energy state a to a higher energy state b:
$$E_{a\to b}=E_b-E_a\quad(a<b)$$
Ionization energy
- An atom may be raised to the n = ∞ state or above by absorbing high enough energy
- In this case, the orbiting electron is completely taken away from the atom, i.e. the atom is ionized
再討論 Absorbing photons
由energy level 去 energy level，electron只能吸收對應能量的photons。
不過，有energy level 去 ionized state，electron可以吸收photo你擁有該energy level 與 E∞之間的能量差或比這個能量多的photon。
就是説，ionize之後已經不再是quantize，而是continuous。
例如：
在hydrogen atom 中，有一粒electron在第一層，該Level能量 = -13.6 eV
如果這粒electron想跳到第二層，第二層Level能量 = -3.4 eV
這裏electron只能吸收photon有 = -3.4 – (-13.6) = 10.2 eV的能量值
如果這粒在第二層的electron想ionize，它要吸收photon至少有 0 – (-3.4) = 3.4 eV
不過在ionize之後已經不在是quantize，已經沒有數值限制，因此這粒electron如果想ionize，可以吸收 3.4 eV, 3.5 eV, 3.6 eV……的photon
Lyman series Balmer series Paschen series
這三個series 其實只是將2粒，3粒，4粒的electron所emit的photon frequency group在一起。
Excitation by collision
Apart from absorbing a photon, an atom can be excited by colliding with another particle, such as a fast-moving electron
Elastic Collision
- The incident particle does not possess enough KE to excite the atom
- The particle will be deflected by the atom without any loss in KE
Inelastic Collision
- The incident particle possesses high enough KE to excite the atom
- The atom will absorb partial KE and jump to a higher state
- The particle loses KE = the energy difference between the initial and final energy states
不過level energy 依然是quantized
Aurora
- Energetic particles coming from space collide and excite the oxygen and nitrogen atoms in the Earth’s atmosphere
- When these atoms return to the ground state, the oxygen atoms usually emit green and red light; the nitrogen atoms usually emit blue light
Chapter 3 Nanotechnology
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Wave–particle duality of matter
light is both a wave and a particle.
- Wave: undergoes diffraction & interference
- Particle: can only be emitted/absorbed in whole no. of photons
de Broglie wavelength λ
$$\lambda=\frac hp=\frac h{mv}$$
- λ of volleyball (~10−34 m) ≪ door gap (~1 m)
⇒ diffraction not observable - λ of electron (~10−10 m) ≈ spacing in crystal (~10−10 m)
⇒ diffraction observable
Matter wave of an orbiting electron
- Free electron:
λ can take any value - Orbiting electron:
λ can only take a set of particular values
\begin{aligned}&\text{Bohr’s quantum condition: }mvr=\frac{nh}{2\pi}\\&\Rightarrow\quad\lambda=\frac h{mv}=\frac{2\pi r}n=\frac{2\pi(n^2a_0)}n=n\cdot2\pi a_0\quad(a_0=\text{Bohr radius})\end{aligned}
Electron diffraction
- G. P. Thomson transmitted electrons through a metal foil
- Produced diffraction rings
Electron interference
- Electrons also give an interference pattern similar to light
- Confirms that electrons exhibit wave-like properties
Nanoscale
means size as small as 1 nm to 100 nm
Resolving power
ability to form distinct images of two objects that are close together
min. resolvable angular separation
$$\theta_{\min}\approx\frac{1.22\lambda r}D\quad\text{(in radian)}$$
Transmission electron microscopes (TEM)
- Uses electron waves instead of visible light
- Electrons used have wavelengths about 10−12 m
- Min. resolvable length is about
0.1–0.5 nm
higher voltage ⇒ smaller λ ⇒ higher resolving power
TEM Structure
- electron gun
- condenser magnetic lens
- specimen
- objective magnetic lens
- projection magnetic lens
- screen
Limitations of TEM
- Only specimens thin enough for electrons to pass through
(< 500 nm thick) can be examined - Specimen may be damaged by electron beam
- Only 2-D images of internal structure of the specimen can be produced
Scanning tunnelling microscopes (STM)
- A tiny probe tip is put very close to the specimen (<1 nm)
- Small voltage is applied across the tip & the surface
- Some electrons have a chance to jump across the vacuum gap (due to quantum tunnelling)
- Create a tunnelling current
Comparison between the TEM and STM
| Technique | Observation | Specimen Function Requirement | Minimum Resolvable Length | Images Produced |
|---|---|---|---|---|
| STM | Surface structures | Electrically conductive on its surface | lateral：10-10m vertical：10-11m | 2D and 3D |
| TEM | Internal structures | Thin enough | 10-10m | 2D only |
Gold
Gold in its bulk form
Yellow in colour
Gold nanoparticles
Red when suspended in water
ZnO
ZnO in its bulk form
- White in colour
- Reflecting all types of visible light
ZnO nanoparticles
- Transparent
- Provide stronger protection against UV radiation
Surface effect
- Properties of bulk form are dominated by interior atoms
- Properties of nanoform are dominated by surface atoms
Recent developments in nanotechnology
Self-cleaning coatings
Hydrophilic coating
- water-attracting
- attracts water molecules to form
water film on the glass
Hydrophobic coating
- water-repelling
- water droplets on it form globules
- A thin layer of transparent TiO2 nanoparticles
- Self-cleaning process comprises two stages:
- Photocatalytic stage
Under sunlight, TiO2 speeds up break down of dirt particles
- Hydrophilic stage
- When it rains, rainwater falling on glass spreads out to form a water film
- The film washes the dirt particles away easily
Physics 必修課題
- Temperature and Thermometers
- Heat Capacity
- Change of State
- Gas laws and Kinetic Theory
- Motion
- Force
- More about Force
- Work Energy and Power
- Momentum
- Projectile Motion
- Uniform Circular Motion
- Gravitation
- Wave Motion
- Reflection Refraction and Diffraction
- Interference and Stationary Waves
- Light and Sound
- Reflection of Light
- Refraction of Light
- Lenses
- Electrostatics
- Circuit and Power
- AC and Domestic Electricity
- Electromagnetism
- Electromagnetic Induction
- Radiation and Radioactivity
- Rate of Decay and Uses of Radionuclides
- Nuclear Energy