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Extra Nuclear Structure Photoelectric effect ( 光電效應 ) • Evidence of light quanta 光量子的證明 • Introduction of the concept of photons 光子 • wave – particle duality of light Light is wave(EM wave): Proof: Young’s double slit experiment Light is also particle, called photon. Proof: photoelectric effect Light electrons Photocurrent K A Photocell K= Cathode, emitter A = Anode, collector Light K Photocurrent A Photocell K=(photoelectrons Cathode, emitter Electrons 光電子 ) are = Anode,metal collectorsurfaces when ejectedA from EM radiation of high enough frequency falls on them.頻率足夠高 的電磁輻射 光電流 臨閾頻率 Now we try to study the effect of frequency 頻率 & intensity 光強度 of EM radiation in this phenomenon. By changing the position of the sliding contact on the potentiometer, we can change V, voltage across the photocell. Light I, f A I Voltmeter: measure V +V : higher voltage at A Microammeter: Measure photocurrent I 8 V 0V +12 V I P3 P2 P1 -VS 0 Same f Different intensity V •I No. of photoelectrons reaching A •V > 0, I = constant all photoelectrons reach A •When V = 0, I 0 electrons emitted are having KE. I P3 P2 P1 -VS 0 V V<0 electrons will be decelerated by the E-field some of them will even be rejected back to K. At V = -VS (stopping potential遏止電勢 ), I = 0 the most energetic (highest KE) electrons just fail to reach the collector A By energy conservation, the stopping potential and the maximum KE of the photoelectrons are then related by the equation W.D. by E-field = loss of KE eVS = KEmax 0V -Vs K KEmax e- KE=0 A e- E-field I P3 P2 P1 -VS 0 V • P1, P2, P3 :different intensities of incident light with the same frequency • P1 < P2 < P3. • For same f, intensity I I f1 f2 f3 -VS3 -VS2 -VS1 0 V Different frequency: f3 > f2 > f1 V S 3 lines for 3 different metals 0 f f " 0 f ' 0 f 0 f Vs (more –ve stopping potential) The black dashed line is not the result of the experiment. It is just an extension. y = mx + c Vs = hf + c Vs = hf hf0 KEmax = hf F Laws of photoelectric emission ( 光電發射效應 ) 1. No. of photoelectrons intensity 2. f KE of electron (Vs) independent of intensity 3. For a given metal, minimum fo , threshold frequency臨閾頻率 for f < fo , no photoelectron Failure of classical wave theory 波動理論 Wave theory: Predictions by wave theory Energy intensity Intensity KE (Vs) exp. result: KE is independent of intensity large enough intensity e must escape exp. result: existence of threshold frequency fo e is small Take time to absorb energy exp. result: no time delay Einstein’s explanation Einstein suggested that light have dual nature. During transmission, they behave as waves. When they are emitted or absorbed, they behave as particles. He assumed that EM radiation consists of lumps of energy called photons 光子. Energy of photon E = hf f = The frequency of light h = 6.625 1034 J s = Planck constant ( 普朗克常數 ) Einstein’s photoelectric equation KEmax = hf F KEmax : Max KE of photoelectron hf : energy of photon with frequency f F: Work function The intensity of light nhf n = No. of photons No. of photoelectrons Photocurrent since each photon is absorbed by one electron (1) (2) If hf > work function F , photoelectrons will be emitted instantly. There should not be any time lag. F hf0 = F f 0 h I double P, same f P, f same P, double f 0 Intensity P nhf Same P, double f V P (n/2) h (2f) n n/2 photocurrent halved The most energetic photoelectrons, KE = KEmax • absorbed the energy of the photons, hf • jump out of the metallic surface directly, without losing their energy in making collision with other particles inside the metal • except in overcoming the surface barrier of the metal.(work function 功函數 F ) KEmax = hf F or KEmax = hf hf0 VS 0 slope = h/e f f0" f0' F/e f0 eVS = Kemax KEmax = hf F eVS = hf F h F VS f e e Application of photoelectric effect Light-dependent resistor / Photocell / photoelectric cell: 1. Reproduction of sound from movie films 2. As a light-sensitive switch 3. To be a count detector (conveyor belt) AL MC 99-40 AL MC 00-41 AL MC 01-39 AL MC 02-35 Energy levels of hydrogen atom 氫原子的能級 •Line spectra of monoatomic gases •Explanation in terms of light quanta (photons) & energy levels •Hydrogen spectrum: energy level equations En = -13.6/n2 eV Why H atom? H atom is the simplest atom. H atom contains one electron only. H atom is the only atom so far scientist can fully understand and explain its orbital electron motion and energy levels. He atom is already too complicated. Emission & absorption spectra 發射光譜 和吸收光譜 • Atoms in a substance can be excited when the substance is heated, bombarded by electrons or illuminated with radiation. • These excited atoms return to lower energy states accompanying with emission of radiation. • monoatomic gas line spectrum Energy Levels 能級 of hydrogen atom氫原子 Spectrometer Energy Levels 能級 of hydrogen atom氫原子 Hydrogen spectrum (visible part) 400nm 500nm 600nm Balmer series: n = 2 700nm Energy levels of hydrogen atom n = 1: n E / eV 0 4 3 0.85 1.51 2 3.40 ground state n = 2: 1st excited state n = 3: 2nd excited state : : : : 1 13.6 Discrete lines in hydrogen spectrum Existence of energy level in hydrogen atom The value of the allowed energy levels能 級 of atomic hydrogen is: 2.176 10 En 2 n 13.6 E n 2 eV n n = 1, 2, 3, ……… 18 J or n 13.6 E n 2 eV n n = 1: E1= -13.6 eV ground state基態 (lowest energy state) n = 2: E2= -3.4 eV 1st excited state n = : E = 0 eV H atom is ionized. Electron is escaped from the atom Ionization energy電離能 of atom • The least energy required to remove an electron completely from an atom in ground state. • Also called binding energy of the atom • Electron: E1 E • For H atom, ionization energy = E- E1 = 0 – (-13.6) = 13.6 eV Transition of electron in H atom • In H atom, an electron can move from energy level En to energy level Em with an energy change E = Em - En . m • For m > n, E = Em - En > 0 energy is increased (absorb energy) n e • For m < n, E = Em - En < 0 n e energy is decreased (release energy) m • a photon with energy E will be absorbed but photons with energies other than E will be scattered away. e.g. photon with E = hf = 10.2 eV (photon is absorbed & electron transition from E1 to E2) photon with E = 11.5 eV (scattered away & no e transition) However, a photon of energy greater than ionization energy電離能 will be absorbed and the extra energy will store as the initial KE of the escaped electron逃逸電子的初動能 . E.g photon with E = 20.6 eV > 13.6 eV photon is absorbed H atom is ionized (e escape逃逸 ) KE of escaped e = 7.0 eV • Apart from photons, electrons and other particles can also excite other atoms by bombardment. Just like the collision of snooker balls. Energy is transferred from one ball to the other. • E.g. In Franck-Hertz experiment ( 法蘭赫茲 ), we use energetic electron to excite atoms Excited atoms (n > 1) • lasting no longer than a ms (short time) • finally return to its ground state • associated with the emission of one or more photons. Wavelength of the emitted/absorbed photon: hf E E n E m hc 13.6 13.6 ( 2 ) ( 2 ) n m 1 13.6 1 1 2 2 hc n m Easier to remember that 18 2.176 10 E J or n 2 hf = E = |Enm – En| 13.6 E n 2 eV n e move from energy level En to Em f : frequency of photon absorbed or emitted AL MC 01-40 AL MC 02-37 AL MC 02-36 AL MC 98-42 Franck-Hertz experiment ( 法蘭克赫茲 ) • Evidence for energy level能級 • Excitation energy激發能 • Elastic and inelastic collisions of electrons with atoms • Principle of Franck-Hertz type experiments. VG >VK VP < VG (slightly) Gas atoms (e.g. Hg 汞 atoms) at low pressure K G electron P • Thermionic emission • Accelerating voltage can be varied. • the accelerating voltage (between G & K) must be larger than the retarding potential減速電勢(between G & P). VG - VK > VG – VP • Typically, VG - VP 1V • I (microammeter) amount of electrons reach P Suppose that at the ground state, the outermost electron of the Hg atom is in the electron shell n. Energetic electron collide with Hg atom n+2 n+1 eVi KE = eVGK n eVj Hg atom Results: Vi, Vj = The excitation potentials of the atom I 0 V i Vj 2Vi 2Vj3Vi V In the notes, V = VGK is measured by the voltmeter. for V < VGP (retarding potential), I = 0 For VGP < V < Vi, V I elastic collision彈性碰撞 e have no KE loss At V = Vi, I drops rapidly inelastic collision e lose all KE atoms is excited For Vi < V < Vj, I again as V V – Vi > retarding potential e reach P At V = Vj, I drops rapidly again inelastic collision e lose all KE atoms is excited (another energy level) At V = 2Vi, 2Vj, 3Vi, 3Vj, Vi + Vj,……… I drops successive inelastic collisions with 2 or more atoms Most likely, in Franck-Hertz experiment, we get the following result. The result depend on the gas density and the temperature of the gas. AL MC 00-40 Ionization energy (ionization by collision) When the H atoms are ionized (13.6V), H ions (+ve ion) are attracted to the anode. Line spectra (線狀光譜 ) • monatomic gases單原子氣體 only • The line spectrum of a gas consists of the characteristic lines of the gas • 一氣體的明線光譜是該氣體的特徵線 Line spectra (線狀光譜 ) EHT In a gas discharge tube ( 放電管 ) a high voltage ( 1 kV ) is applied across electrodes in a tube containing a low pressure gas. diffraction grating discharge tube Results(observation): 1. There are lines of discrete frequencies f radiated in emission spectrum. 2. Emission lines ( 發射線 ) are closer at lower end (shorter wavelength) of the spectrum. 3. Intensities of lines are different. He emission spectrum 400nm 500nm 600nm 700nm Production mechanism產生機制 • Gas atoms are excited by the bombardment of bullet electrons, or by heating. e transit to higher energy level (較高能級) • electron: higher energy level En a lower energy level Em • Emission of radiation then occurs • a photon of frequency f = ( En Em )/h is emitted. explanations The energy levels are getting closer and closer for higher energy state. the emission spectrum is discrete and lines are closer at lower end. (short wavelength) The intensities of lines depend on transition probability躍遷的機會率 . For line spectra, the emissions are mostly spontaneous自發 的 . different intensities Absorption spectrum ( 吸收光譜 ) • When white light passes through “cool” dilute gases, and absorption spectra will be obtained. • “cool” does not glow most atoms at ground state cotton wool white light source iodine vapour diffraction grating He emission & absorption spectrum ‘Dark’ lines because they are not as bright as the ‘unabsorbed’ light. H absorption and emission spectrum The emission and absorption spectra of the same element are complementary to one another. Production mechanism • Only photons of certain frequencies f = ( En Em )/h can excite the corresponding gas atoms. • The excited atoms will return to ground state quickly. • For the other photons (other frequencies), they just pass or are scattered away. explanation • The atoms of the gas absorb incident photons of certain wavelength and re-emit photons of the same wavelength almost immediately, but in all directions. • Consequently, the intensity of light of these wavelengths, in the original direction is reduced and ‘dark’ lines are produced. Continuous spectra ( 連續光譜 ) • In solid, liquid and compressed (dense) gas continuous spectra • Molecular gases or chemical compounds band帶狀 spectra • excited atoms or molecules are not wholly independent of one another, energy levels of the atoms will have interaction among them. radiation of more wavelengths are emitted. Continuous spectra ( 連續光譜 ) • The spectra produced by a hot filament wire or the sun is continuous. • Because at high temperature, there is obvious interaction between atoms as a result of overlapping of energy levels between atoms. Fraunhöfer lines ( 夫琅和費譜線 ) • a series of dark absorption lines in solar spectrum vaporized elements • light from the core of the sun (photosphere), passing through the chromosphere色球 (the solar atmosphere 太陽大氣層 ), is absorbed selectively by the relatively cool gases in it. Fraunhöfer lines ( 夫琅和費譜線 ) • Fraunhöfer lines are readily observable before an eclipse takes place, because the chromsphere is only visible when the light from the photosphere is blocked by moon. • hydrogen, helium, sodium氫、氦、鈉 etc, in the chromosphere X-rays (X 射線) • • • • • Production & properties Maximum frequency X-ray spectra Energy interpretation of line spectra Uses in medicine, industry & crystallography Properties of X-rays: • High penetrating power ( 貫穿能力 ) • High ionization power ( 致電離能力 ) • High frequency EM wave Effect of X-rays on human body • • • • Deep-seat burns Destruction of living cells Unpredictable chemical changes Genetic changes Applications of X-rays • Medical uses in diagnosis and therapy • X-ray crystallography in analysis of molecular structure • Industrial radiography in locating internal imperfections. • Inspection of suitcases at airports How to produce EM wave? One of the ways: When a charged particle is accelerating, EM radiation (energy) is released. X-ray: high energy EM radiation require high acceleration In physics, acceleration is the same as deceleration. Production using X-ray tube X射線管 _ high voltage + V filament target electrons filament leads anode cooling liquid Evacuated glass tube X-rays • electrons emitted from the hot filament • Electrons are accelerated by a high voltage V ( >6 kV 1MV). high velocity • X-rays are emitted when the target metal (a metal of high atomic number e.g. tungsten ) in the anode is bombarded by these electrons. (deceleration) • Target metal of high atomic number numerous electron shells X-rays of high frequency Cooling system prevent the target from melting X-ray spectrum (X射線譜) • continuous spectrum ( 連續譜 ) • a line spectrum ( 線狀譜 ) • Minimum wavelength min (highest frequency) Relative intensity Line spectrum Continuous spectrum K L min Production mechanism for continuous spectrum • due to the deceleration of the bombarding electrons • The energies of the emitted x-ray photons equal to the lost KE of the bombarding electrons during deceleration. (conservation of energy) • different electrons lose different amount of energy by having one or more collisions minimum wavelength 波長最小值 min • an electron loses its KE completely in a single collision • all its KE is converted into just one X-ray photon 1 2 c mv eV hf h 2 min min hc eV V: accelerating potential 1 2 c mv eV hf h 2 min min hc eV • For V = 500000 V, min = 0.02484 Å • a TV tube of V = 25000 V, min = 0.497 Å • Higher V shorter min Higher energy Production mechanism for line spectrum • the inner shell electrons of the target atoms being knocked out by the bombarding electrons (inner e move to higher energy levels) • followed by the transitions of the outer shell electrons to fill the inner vacancies. • Photons of definite frequencies are emitted某 些確定頻率的光子 Production mechanism for line spectrum N M X-ray photons K L K K factors affecting the X-rays spectrum • Temperature of filament 燈絲的溫度 intensity • Accelerating voltage V min & intensity • Material target metal 靶的物質 different line spectra but same min Laser激光 • Light Amplification by Stimulated Emission of Radiation (LASER) 受激輻射的光放大激光的作用 • Brief qualitative discussion of laser action • The uses of lasers Properties of laser • • • • • • Monochromatic單色光 (single frequency) Coherent相干 High intensity高強度 Long coherent length (a few meter) Beam is parallel / uni-directional單向性 (some laser can produce polarized radiation) 偏振 Spontaneous emission ( 自發發射 ) • An excited atom falls back to its ground state randomly.受激原子會隨機地回落到基態 • The radiation emitted is incoherent ( 不相干 ) & in all directions. • The probability of spontaneous emission is proportional to the number of excited atoms. • It occurs in light bulb燈泡, discharge tube放 射管 etc. Stimulated emission ( 受激發射 ) • a photon of energy hf , where hf = En E1 is capable of stimulating a excited atom to pass from an excited state to the ground state. (electron: En E1) En Photon: hf E1 The probability of stimulated emission depends on • the no. of excited atom • the no. of photons of energy hf available difficulty • Stimulated emission doesn’t happen easily • Naturally, most atoms are at ground states • Solution : population inversion Population Inversion ( 粒子分佈倒置 ) • Population inversion is a situation where the majority of atoms are excited to a higher state. (higher energy level) 大部份的原子是在受激態的情況 • This state must be a metastable state ( 亞 穩 態 ) in which the electrons remain longer than usual (~3ms) • the transition to the lower state occurs by stimulated emission rather than spontaneous emission. Ground state: electrons occupy the lowest energy levels Population inversion: More electrons are at higher energy level P(stimulated emission) > P(absorption) En hf = En - E1 E1 Production mechanism • Atoms are excited to an unstable energy level by absorbing photons of flashes of light (optical pumping). • Population inversion occurs when excited atoms reach metastable state (by emitting photons hf1. ) • Apart from optical pumping, there are other ways of pumping, like electrical pumping in CD & DVD players (pumping) stimulated absorption of a photon of hf = Em E1 spontaneous emission of a photon of hf1 = Em En excited state Em metastable state En ground state E1 • Some of the excited atoms in metastable state emit photons hf2 spontaneously. • These photons stimulate the emission of other photons of same frequency f2 (light amplification) and in phase. stimulated emission by photon of hf2 = En E1 atom 1 atom2 electron n hf2 (n+1) hf2 (n+2) hf2 mirror Optical pumping: Laser beam partial mirror • As the process continues, large number of photons is built up ( also due to the fact that light is reflected between the two end mirrors.) • The coherent laser beam is emitted from a small hole of one of the mirror to be more unidirectional. applications • Optical fibre communication, Laser diode for telephone communication • Printing • reading digital information (DVD, CD….) • Ranging, Welding, Drilling, Pointer for instructor, Holography • Cutting of cornea for short, long sight, Treatment of detached retina