光 電 效 應 實 驗光 電 效 應 實 驗

The Interaction of Radiation with Matter( 電磁輻射與物質之間作用 ) The Photoelectric Effect ( 光電效應 ) The Compton Effect ( 康卜吞效應 ) The Pair Production ( 電子偶產生 ) The incident light (Photon) is completely absorbed by the atomic electron. Scattering of photons (x-rays) from free electrons. The disappearance of a photon ( γ -rays), followed by the appearance of an electron and an positron, with the presence of the nucleus.

Scattering of photons (x-rays) from electrons. Compton shift The Compton Effect ( 康卜吞效應 )

Pair Production ( 電子偶產生 ) A photograph of pair production produced by 300 MeV gamma rays striking a lead sheet The minimum energy to create the pair is MeV The excess energy appears as kinetic energy of the two particles

Photoelectric Effect ( 光電效應 ) The photoelectric effect occurs when light incident on certain metallic surfaces causes electrons to be emitted from those surfaces The effect was first discovered by Hertz The incident light (Photon) is completely absorbed by the atomic electron.

Photoelectric Effect Apparatus When the tube is kept in the dark, the ammeter reads zero When plate E is illuminated by light having an appropriate wavelength (frequency), a current is detected by the ammeter The current arises from photoelectrons emitted from the negative plate (E) and collected at the positive plate (C) Active Figure 28.7 Active Figure

光電效應 光電子的動能與照射光強度之間有何關 係 ? 光照射金屬表面，照射多久才能產生光 電子 ? 光電子的動能與照射光的頻率之間有何 關係 ?

古典電磁學

Photoelectric Effect, Results At large values of  V, the current reaches a maximum value All the electrons emitted at E are collected at C The maximum current increases as the intensity of the incident light increases When  V is negative, the current drops When  V is equal to or more negative than  V s, the current is zero (V0)(V0) (V0)(V0)

Photoelectric Effect Feature 1 光電子的動能與照射光強度之間有何關係 ? Dependence of photoelectron kinetic energy on light intensity Classical Prediction Electrons should absorb energy continually from the electromagnetic waves As the light intensity incident on the metal is increased, the electrons should be ejected with more kinetic energy Experimental Result The maximum kinetic energy is independent of light intensity The current goes to zero at the same negative voltage for all intensity curves 古典電磁學之預估與實驗結果

Photoelectric Effect Feature 2 光照射金屬表面，照射多久才能產生光電子 ? Time interval between incidence of light and ejection of photoelectrons Classical Prediction For very weak light, a measurable time interval should pass between the instant the light is turned on and the time an electron is ejected from the metal This time interval is required for the electron to absorb the incident radiation before it acquires enough energy to escape from the metal Experimental Result Electrons are emitted almost instantaneously, even at very low light intensities Less than s 古典電磁學之預估與實驗結果

Photoelectric Effect Feature 3 光電子的動能與照射光的頻率之間有何關係 ? Dependence of ejection of electrons on light frequency Classical Prediction Electrons should be ejected at any frequency as long as the light intensity is high enough Experimental Result No electrons are emitted if the incident light falls below some cutoff frequency, ƒ c The cutoff frequency is characteristic of the material being illuminated No electrons are ejected below the cutoff frequency regardless of intensity 古典電磁學之預估與實驗結果

Photoelectric Effect Feature 4 光電子的動能與照射光的頻率之間有何關係 ? Dependence of photoelectron kinetic energy on light frequency Classical Prediction There should be no relationship between the frequency of the light and the electric kinetic energy The kinetic energy should be related to the intensity of the light Experimental Result The maximum kinetic energy of the photoelectrons increases with increasing light frequency 古典電磁學之預估與實驗結果

Photoelectric Effect Features, Summary The experimental results contradict all four classical predictions Einstein extended Planck’s concept of quantization to electromagnetic waves All electromagnetic radiation can be considered a stream of quanta, now called photons A photon of incident light gives all its energy hƒ to a single electron in the metal ( Photon Model )

Photons( 光子 ) 光子能量 E=hf 光子動量 p = h /λ 電子能量 E 2 = (pc) 2 + ( m e c 2 ) 2 m e = 靜止質量, p = 動量, c = 光速

Photoelectric Effect, Work Function Electrons ejected from the surface of the metal and not making collisions with other metal atoms before escaping possess the maximum kinetic energy K max K max = hƒ – W 0  K 為光電子的動能  W 0 is called the work function The work function represents the minimum energy with which an electron is bound in the metal ( Photon Model )

Photon Model Explanation of the Photoelectric Effect Dependence of photoelectron kinetic energy on light intensity K max is independent of light intensity K max depends on the light frequency and the work function The intensity will change the number of photoelectrons being emitted, but not the energy of an individual electron Time interval between incidence of light and ejection of the photoelectron Each photon can have enough energy to eject an electron immediately

Photon Model Explanation of the Photoelectric Effect, final Dependence of photoelectron kinetic energy on light frequency K max = hƒ – W 0 There is a failure to observe photoelectric effect below a certain cutoff frequency. Without enough energy, an electron cannot be ejected, regardless of the light intensity

Cutoff Frequency The lines show the linear relationship between K and ƒ The slope of each line is h The absolute value of the y-intercept is the work function The x-intercept is the cutoff frequency( f c =W 0 /h ) This is the frequency below which no photoelectrons are emitted - W 1 - W 2 - W 3 K max = hƒ – W 0 K max = eV 0 = hƒ– W 0 V 0 = (h/e)ƒ – W 0 /e

當反向電壓增加至 V 0 ( 截止電位 ) 使光電流降為零時, K max =eV 0

Cutoff Frequency The lines show the linear relationship between V 0 and ƒ The slope of each line is h The absolute value of the y-intercept is the work function The x-intercept is the cutoff frequency This is the frequency below which no photoelectrons are emitted - W 0 /e 1 - W 2 - W 3 K max = eV 0 = hƒ– W 0 V 0 = (h/e)ƒ – W 0 /e V0V0

利用電容測量截止電位 Active Figure

講義結束

Scattering of photons (x-rays) from electrons. Compton shift The Compton Effect ( 康卜吞效應 )

The Compton Effect 入射光子能量 E=hf 0 入射光子動量 p = h /λ 0 x y 散射光子能量 E=hf  散射光子動量 p = h /λ  電子動量 p e 靜止的電子 電子能量 E 2 = (pc) 2 + ( m e c 2 ) 2

The Compton Effect x y 電子動量 p e 電子能量 E 2 = (pc) 2 + ( m e c 2 ) 2 (1) (2) (3)

(1) (2) (3) 整個 (1) 式整理後取平方 整個 (2) 式取平方

(3) 整個 (3) 式整理後取平方 (4)

整個 (4) 式代入 (4) 整理後 Compton shift

Some Work Function Values