4.4.3 Experimental principles
Planck constant(recognized value h=6.626 19×10-34 J·s)is an important and universally applicable constant in nature,and it is a universal constant related to blackbody emission and absorption introduced by Max Planck(1858—1947),which can be measured simply and accurately by the photoelectric effect.
When a certain frequency of light shines on some metal surfaces,the electrons in the metal absorb the energy of the light and escape from the metal surfaces.This phenomenon is the photoelectric effect.The study of the photoelectric effect has made people further realize the nature of the wave-particle duality of light,and promoted the establishment of the quantum theory of light and the development of modern physics.
The experimental device of the photoelectric effect principle is shown in Figure 4.4.2.Where K is the cathode of the phototube,A is the anode,I is the current flowing through the microammeter,and the reading of the voltmeter is U0.When the light with a frequency higher than a certain“red limit ν0”and intensity of P shines on the metal surface,only part of the energy of the light is absorbed by the object in the form of heat,and the other part is converted into the energy of some electrons in the object,allowing the electrons to escape from the metal surface.
Figure 4.4.2 Schematic diagram of photoelectric effect circuit structure
Figure 4.4.3 The volt-ampere characteristic curve of the photocell at the same frequency and different light intensity
Figure 4.4.4 The volt-ampere characteristic curve of the photocell at different frequency
Figure 4.4.5 The cut-off voltage versus incident light frequency
The basic experimental rules of the photoelectric effect can be summarized as:
(1)The relationship between the photocurrent I and the potential difference UAK across the phototube is shown in Figure 4.4.3.It can be seen from the figure that there is a voltage U0corresponding to a certain frequency.When UAK≤U0,the photocurrent is zero.This anode voltage U0,which is a negative value relative to the cathode and is called the cut-off voltage;when UAK≥U0,the photocurrent I increases rapidly and then tends to saturation.The saturated photocurrent IM is proportional to the intensity P of the incident light.
(2)For light of different frequencies,the cut-off voltage is different,as shown in Figure 4.4.4.
(3)When the frequency of the incident light is lower than a certain frequency,no photoelectrons are generated regardless of the incident light intensity.This frequency is called“threshold frequency ν0”or“cutoff frequency”,as shown in Figure 4.4.5.When the frequency of the incident light is higher than the cutoff frequency,the initial kinetic energy of the photoelectron is proportional to the frequency of the incident light,and has nothing to do with the intensity of the incident light.
(4)The photoelectric effect is a transient effect.When light above the threshold frequency is irradiated on the cathode,no matter how weak it is,photoelectrons are generated almost at the beginning of the irradiation,and the delay time does not exceed 10-9 seconds.
The above-mentioned experimental laws cannot be fully explained by light wave theory.
In 1905,Albert Einstein put forward the theory of light quantum,which successfully explained the phenomenon of the photoelectric effect.He believed that a beam of light with frequency ν is a stream of particles with energy hν moving at the speed of light.These particles are called light quanta,or photons for short,and h is called Planck constant.
Einstein believed that the light emitted from a point of frequency ν is radiated out one by one in the form of hν as the energy units(light quanta),rather than as Maxwell’s electromagnetics points out that light is a continuous distribution of energy from spreading energy to space.When the light of frequency ν acts on a free electron in the metal with hν as the unit,after the free electron gains energy,it overcomes the work function WS=eU0 of the metal surface,and then escapes the metal surface,and its initial kinetic energy is 1/2 mV2.According to energy conservation:(https://www.daowen.com)
Where h is Planck constant;ν is the frequency of incident light,m is the mass of electrons;V is the initial velocity of photoelectrons escaping from the metal surface,WS is the work function of the metal material irradiated by light.
It can be seen that the greater the frequency(ν=c/λ)of the light incident on the metal surface,the greater the maximum initial kinetic energy of the escaped electrons(WS remains unchanged).It is precise because the photoelectron has the maximum initial kinetic energy.When the acceleration potential difference UAK=UA-UK=0,there are still photoelectrons falling to the anode to form a photocurrent.Even when the potential of the anode is lower than the potential of the cathode,there will be photoelectrons falling to the anode.Until the acceleration potential difference is a certain negative value U0,all photoelectrons cannot reach the anode,and the photocurrent is zero.This U0 is called the cut-off potential(or cut-off voltage)of the photoelectric effect.At this time:
Substituting Equation(4.4.2)into Equation(4.4.1)formula,we have:
Since the work function WS of a metal material is an inherent property of metal.For a given metal material,WS is a fixed value,independent with the frequency of incident light.Let WS=hν0,where ν0 is threshold frequency(red limit frequency),that is,the energy of a photon with threshold frequency ν0 is exactly equal to work function WS,and when there is no excess energy.Equation(4.4.3)is rewritten as:
The Equation(4.4.4)shows that the cut-off potential U0 is a linear function of the incident frequency ν.When the frequency of the incident light ν=ν0,the cut-off voltage U0=0,and no photons escape.Then slope of the above formula
is a normal number,so:
It can be seen that as long as the U0-ν linear line at different frequencies is made by experimental methods,and the slope of the linear line is obtained,the value of Planck constant h can be calculated by Equation(4.4.5)(the electric quantity of electrons e=1.602×10-19 Coulomb),the red limit frequency and work function of the cathode material of the phototube can be calculated in turn.
Figure 4.4.6 Measured volt-ampere characteristic curve of photocell
Therefore,the key to measure the Planck constant by using the photoelectric effect method is to obtain monochromatic light.Then measure the volt-ampere characteristic curve of the phototube and determine the cutoff potential difference.
The experimentally measured photoelectric cell volt-ampere characteristics are shown in Figure 4.4.6,which is more complicated than that shown in Figure 4.4.4,mainly because the actual measurement of the photocurrent also contains the following currents.
(1)Dark current and background current:The dark current is the electron flow that is generated when the photocathode is not exposed to light due to the thermal movement of electrons and the leakage of the photoelectric cell shell.The background current is generated by various stray lights.The photocurrents also change withthe change of the applied voltage.
(2)Anode photocurrent:When making a photocathode,the anode will also be sputtered onto the photocathode material,so as long as there is light hitting the anode,the anode will also emit photoelectrons to generate anode current.
In fact,the current value of each point on the measured curve(solid line)is the algebraic sum of several other current values.Obviously,the voltage value corresponding to the point on the curve where the photocurrent is zero is not the cut-off voltage.The real cut-off voltage should be the point C of the actually measured curve is the point where the oblique straight part meets the curve part.This method is called the“inflection point method”.
