Study of Photoelectric Effect

The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner can be called photo-electrons.

According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. From this perspective, an alteration in either the intensity or wavelength of light would induce changes in the rate of emission of electrons from the metal. Furthermore, according to this theory, a sufficiently dim light would be expected to show a time lag between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by classical theory.

Instead, electrons are only dislodged by the impingement of photons when those photons reach or exceed a threshold frequency. Below that threshold, no electrons are emitted from the metal regardless of the light intensity or the length of time of exposure to the light. To make sense of the fact that light can eject electrons even if its intensity is low, Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy hf. This shed light on Max Planck’s previous discovery of the Planck relation (E = hf) linking energy (E) and frequency (f) as arising from quantization of energy. The factor h is known as the Planck constant :

E = hf = h(c/λ) > W_e

h : Planck Constant
f : frequency
λ : wavelength
c : light speed
W_e : minimum energy threshold

The quantum interpretation of the photoelectric effect is the following :

• An electromagnetic radiation of frequency f carries packets of energy E = hf called photons
• The intensity of the radiation is given by the number n of transported packets
• In the photoelectric effect a photon is completely absorbed by an electron, which increases its energy of an amount equal to hf
• The kinetic energy of the emitted electrons is E_kin = hf – W_e
  • W_e = energy required to extract an electron from the material
  • hf = energy provided by the radiation
• if hf < W → there is not enough energy in order to extract electrons → threshold
• An electron can only receive energy from a quantum → the kinetic energy of the emitted electron does not depend on the intensity of the incident radiation
• increasing the intensity of the radiation increases the number of packets of energy → the number of emitted electrons increases with the intensity
• E_kin = hf – W_e → the energy of the single electron increases as the frequency of the incident radiation

The photoelectric effect provides evidence, in a way not related to the black-body radiation, that the electromagnetic radiation consists of quanta of energy hf.
These experimental facts can be easily verified by measuring the stopping potential V₀, which is the electrical voltage needed to stop the flow of electrons generated by the effect photoelectric :

E_cin = hf – W_e
E_cinmax = eV₀
V₀ = ( hf – W_e )/e

The measurement should be done ​​at different wavelengths.
The values ​​of constants to be used :

h = 6.626×10^-34 Js
e = 1.602×10^-19 C
h/e = 4.136×10^-15 Js/C

Experimental Setup

For the experimental verification of the photoelectric effect, we used the setup described in the following diagram :

As phototube we used the model 1P39 characterized by an anode coated with Sb – Cs with spectral response of type S -4 , suitable for this type of use :

LED Spectra

As photon source we used LED of various colors, whose spectra were acquired with the Spectrometer DIY and with the software Theremino Spectrometer.

Measurements Results

Tipo LED	λ (nm)	Freq. (1014 Hz)	Stopping Voltage (V)
Infrarosso	850	3,57143	NA
Rosso	629	4,76948	0,17
Giallo	589	5,09338	0,32
Verde	530	5.66038	0,67
Blu	470	6.38298	0,88
UV	405	7,40741	1,17

From the linear regression line of the graph above we get the following values ​​of the ratio h/e and the work function :

h/e = 3.9×10^-15 Js/C while the correct value is 4.136×10^-15 Js/C
W_e = 4.218 x h x 10¹⁴ = 1,74eV

The agreement with the correct values ​​seems good.

Pdf document with the complete description of the experiment : EffettoFotoelettrico_ENG

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