Quantum Physics: Photoelectric Effect and Atomic Spectra

Measuring the Photoelectric Effect

The electrons emitted by illuminating the cathode originate an electric current of intensity I upon collision with the anode. This intensity is proportional to the number of electrons ejected. The number of electrons reaching the anode is measured by the current flowing through the ammeter. The work W necessary to eject an electron from the metal depends on its binding energy. The minimum energy required is called the work function of the metal (W₀), defined as: W₀ = h f₀.

If the anode is positive, it will attract electrons; if the anode is negative, electrons will be repelled. In the latter case, the current will only reach the anode if the electrons possess an initial kinetic energy (E_c) sufficient to overcome the repulsive potential.

Photon Characteristics and the Compton Effect

Although Millikan's experiments corroborated Albert Einstein's hypothesis, the confirmation of the existence of photons was provided by the physicist Arthur Compton. He directed a beam of wavelength λ onto a sheet of graphite and observed that the scattered radiation consisted of two wavelengths: one equal to the incident wavelength, λ, and a larger one, λ'.

According to classical theory, the scattered wave should have the same wavelength as the incident wave. However, Compton considered electromagnetic radiation as a set of relativistic particles (photons), each with:

• Zero rest mass (M₀ = 0)
• Energy: E = hf
• Momentum: p = E / c = hf / c = h / λ

The Compton effect confirms both the validity of relativistic mechanics and the existence of photons.

Atomic Spectra and the Rydberg Formula

In the late 19th century, scientists gathered significant data on the light emitted by the atoms of a gas excited by an electric discharge. Spectroscopic analysis of the radiation showed the appearance of a discrete set of lines of different wavelengths.

• Emission Spectrum: Elements emit energy in the form of electromagnetic radiation, but only at a few specific frequencies.
• Absorption Spectrum: Elements absorb specific frequencies when illuminated by electromagnetic radiation.

An element absorbs and emits the same discrete set of frequencies of electromagnetic radiation. This spectrum, whether absorption or emission, is characteristic of each element. Johannes Rydberg studied the spectrum of hydrogen and developed the following expression, known as the Rydberg formula:

1 / λ = R_H (1/m² - 1/n²)