Photoelectric effect

Photoelectric effecT

The photoelectric effect discovered by Hertz in 1887 provides more direct evidence of the quantum theory of light and the particle aspect of radiation.

Definition:The photoelectric effect is the emission of electrons from a metal plate under the effect of light. The energy of this light must be sufficient to be able to tear the electrons from the metal.

The movement of these torn electrons results in a current in an electrical circuit.

Experience:Measure the intensity of the current received by the anode A according to 3 parameters:

- Power P of the incident radiation

- The frequency n(or l= c / n) of the radiation

- The potential difference V=VC-VA

Experimental setup of the photoelectric effect A: Constations expérimentales 1- The photoelectric effect only takes place if,  the frequency n of light: n > n0.  or its wavelength: l <l0.  n0: threshold frequency and l0: threshold wavelength  n0 and l0 depend on the nature of the metal 2- Existence of a stop potential         .FOR n≥n0 The stopping potential of aU0 photocell:This is the voltage that must be applied across the anode and the cathode to stop the current Characteristic I = f (UAC). U0 is negative, it is such that the kinetic energy Ec of the electron torn from the cathode is equal to: Ec = 1 /2 mv² = e|U0| for a given metal, U0 is independent of the power of the radiation 3-Existence of a characteristic IS saturation current for each metal 4- if:n <n0 the photoelectric effect does not appear regardless of the intensity of the radiation and the exposure time. 5- The kinetic energy of the electrons emitted is proportional to the frequency of the radiation n 6-As soon as, n0 <n the intensity of the electric current (number of ejected photoelectrons) is proportional to the intensity of the radiation B: Failure of classical physics to explain the photoelectric effect  The intensity of the electric current I from the electrons ejected by photoelectric effect should be proportional to the light intensity (power) (Which is in contradiction with the fact that I = 0 if n <n0

whatever the power)
 If we increase the intensity of the wave, the kinetic energy of the electrons should increase and the electrons will be ejected.
(Which is in contradiction the fact that the electrons have zero speed if n <n₀ whatever the power)
Disagreement between experimental results and classical physics
“The emission of electrons is instantaneous as soon as n₀ <n. It is as if the wave interacts with the electrons of the metal to pull them out of it.“The emission of electrons is instantaneous as soon as n₀ <n. It is as if the wave interacts with the electrons of the metal to pull them out of it.
"The energy of this wave must be sufficient to extract the electrons from the metal: existence of a threshold frequency n₀ which depends on the nature of the metal;
“The kinetic energy of photoelectrons is independent of the intensity of the radiation, but it is their number that depends on it. (finding 5 and 6)
 the dependence of the kinetic energy of photoelectrons on the frequency of the wave and its independence from the power of incident light cannot be explained by classical theory.

Solution: Einstein (1905)

This effect is an interaction phenomenon

Radiation - Material.

Light = set of corpuscles (Quanta) called photons

energy hn

C: Solution provided by Quantum Mechanics

Einstein's hypothesis: Radiation (light) or electromagnetic radiation consists of a large number of small packets of energy, photons whose energy, for a frequency n is given by:

E=hn=hw= hC/l

Thus, light interacts with matter and it behaves as if the energy were contained in the form of packets located in space. This bundle of energy is called the quantum of light

According to this hypothesis, if the photon has sufficient energy, it can overcome the bond energy of the electron and extract it.

a- Let W0=h n₀  be this binding energy or threshold energy.

b- If n >n₀, the number of ejected electrons increases with the intensity of the incident photons.

c- If n >n₀, the energy balance of the photoelectric effect is hn=W0+EC

Ec=1/2mn²

being the kinetic energy of the photoelectron

The potential to extract electrons from the metal

hn 0= W0= eV0

Threshold energy or extraction energy

The threshold frequency is then given by:

n₀= W₀/h=Ev₀/h

The kinetic energy of the ejected photoelectron EC=hn-w=h(n-n0) Thus, the kinetic energy (or speed) of the photoelectron increases with frequency. La pente détermine expérimentalement la valeur de la constante de Planck h

D: Explanation of Einstein's hypothesis The photon (radiation) interacts with the electrons of the matter During the photon (particle) - electron shock, the quantum of energy hn of the photon is totally absorbed by the electron A part = W0 (extraction work) is used to free the e- The rest is Ec of the e- jected.