Quantum Physics: Key Concepts and Phenomena

Posted on Mar 2, 2025 in Physics

Quantum Physics

1. Thermal Radiation and Black-body Radiation

The electromagnetic energy emitted by a body due to its temperature is called thermal radiation. Thermal radiation varies with temperature and the composition of the body. Bodies whose thermal radiation depends *only* on temperature are said to exhibit black-body radiation and have the following characteristics:

  1. The total power (P) emitted by a surface at temperature (T) satisfies the Stefan-Boltzmann Law: (where σ = 5.67 x 10-8 W/m2K4).
  2. The wavelength at which maximum power is emitted (λmax) is inversely proportional to the temperature (T), according to Wien’s Displacement Law.

2. Planck’s Hypothesis

Atoms that emit radiation behave as harmonic oscillators. Each oscillator absorbs or emits energy in discrete amounts proportional to its frequency of oscillation (f):

E = nhf

Where:

  • h = Planck’s constant = 6.626 x 10-34 J s
  • n = a positive integer (quantum number)
  • f= frequency

These discrete packets of energy (hf) were called quanta, meaning the energy of the oscillators is quantized.

3. Photoelectric Effect

Hertz discovered that when light (visible or ultraviolet) strikes certain metal surfaces, electrons (called photoelectrons) are emitted. This phenomenon is called the photoelectric effect.

Measurements

Electrons emitted from the illuminated cathode create an electric current (I) when they reach the anode. The intensity (I) is proportional to the number of electrons emitted. The work (W) required to remove an electron from the metal depends on its binding energy. The minimum energy required is called the work function (Wo) of the metal.

  • If the anode is positive, it attracts electrons. At a certain positive potential, all emitted electrons reach the anode, and the current (I) is proportional to the total number of electrons.
  • If the anode is negative, electrons are repelled. Only electrons with sufficient initial kinetic energy to overcome the repulsive potential will reach the anode. At a certain negative potential, called the stopping potential (Vs), no electrons reach the anode. The stopping potential multiplied by the electron charge gives the maximum kinetic energy of the photoelectrons.

4. Einstein’s Quantum Theory

According to Einstein, the energy emitted by a radiant source is quantized in packets called photons. To explain the photoelectric effect, Einstein proposed that:

  1. The energy of each photon is related to its frequency by the expression: E = hf.
  2. A photon is absorbed completely by a single photoelectron.

The kinetic energy (Ecmax) of the photoelectron is:

Ecmax = hf – Wo

Where Wo is the work function of the metal.

Einstein’s quantum theory explains aspects of the photoelectric effect that classical physics cannot:

  1. Since the minimum energy required to remove an electron is Wo, when Ecmax = 0, the photon must provide at least an energy Wo = hfo. If the frequency of the radiation is less than fo (the threshold frequency), no photoelectrons can be emitted.
  2. Doubling the light intensity doubles the number of photons and, therefore, the current. This does *not* change the energy (hf) of individual photons or the kinetic energy of each photoelectron.
  3. Because the energy needed to extract an electron is supplied in concentrated packets (photons), there is no significant time delay.