Atomic and Nuclear Physics: Key Concepts and Principles
Blackbody Radiation
Radiant exitance is the energy emitted per unit time per unit area of a body at a certain temperature. The spectral distribution of thermal radiation depends on the nature and state of the radiating surface. A particular pattern is used to study this dependence, this pattern is called a blackbody: it is a body that is capable of absorbing all the radiation incident on it without reflecting anything. The distribution and study of the spectral blackbody emitted at different temperatures is obtained for a family of curves. From these curves, we can draw the following conclusions: the total quantity of energy increases with temperature, and the radiation of maximum intensity moves towards shorter wavelengths as the temperature increases. Both aspects were described by different laws:
- The first law, Stefan-Boltzmann law: The total energy emitted in the unit of time per unit area of a blackbody is directly proportional to the fourth power of the absolute temperature, i.e., W = σ T4, where σ = 5.667 10-8 W/m2 K-4* is the Stefan-Boltzmann constant.
- The second result is described by Wien’s displacement law: The wavelength of radiation for which the energy is maximum is inversely proportional to the absolute temperature.
Photoelectric Effect
The photoelectric effect is the emission of electrons by certain substances (generally metals) when irradiated with electromagnetic radiation of a frequency higher than a characteristic frequency for each substance. Each metal has a minimum frequency of light radiation (f threshold) below which the photoelectric effect does not occur. The number of electrons emitted by the metal is proportional to the intensity of the light radiation received, without affecting the frequency. The emitted electrons have a velocity that depends on the frequency of radiation rather than the intensity. The photoelectric effect is practically instantaneous; it appears and disappears with the radiation. The maximum kinetic energy of the emitted electrons is given by Ecmax = hf – Wl = hf – hf0, where Wl is the work function, h is Planck’s constant, f is the frequency of the incident radiation, and f0 is the threshold frequency.
Planck’s Hypothesis
Planck proposed that light is emitted in discrete and indivisible quantities called quanta, whose energy is proportional to the frequency of the emitted radiation: E = h f, where h is a constant equal to 6.624 10-34.
De Broglie Wavelength
De Broglie proposed that every particle of mass m that moves with velocity v has an associated wave whose wavelength and frequency are given by: λ = h / (m v) = h / p and f = E / h, where h is Planck’s constant, p = mv is the linear momentum, and E* is the energy.
Explanation of the Photoelectric Effect
There are three aspects to study the photoelectric effect that cannot be explained by classical electromagnetic theory:
- The emission of electrons takes place only if the frequency of radiation is greater than a minimum frequency (f0) characteristic of each metal, called the threshold frequency.
- If f is greater than f0, the number of electrons emitted is proportional to the intensity of the incident radiation, but their maximum kinetic energy is independent of the light intensity, which has no classical theory explanation.
- It has never been possible to measure a time delay between the illumination of the metal and the emission of photoelectrons. However, according to classical theory, if the light intensity is very weak, there should be a time delay between the moment the light hits the metal and the emission of photoelectrons.
Bohr’s Atomic Model
The atomic model is a quantized model of the atom proposed in 1913 by Danish physicist Niels Bohr to explain how electrons can have stable orbits around the nucleus. This model is a functional model that represents the atom (physical object) itself and explains how it works by means of equations. Bohr based his model on the hydrogen atom. Bohr tried to create an atomic model that could explain the stability of matter and the discrete emission and absorption spectra observed in gases. He described the hydrogen atom with one proton in the nucleus and one electron orbiting around it. Bohr’s atomic model was based conceptually on Rutherford’s atomic model and the emerging ideas of quantization that had emerged a few years earlier with the investigations of Max Planck and Albert Einstein. Because of its simplicity, the Bohr model is still frequently used as a simplification of the structure of matter. L = n h = n (h/2π).
Uncertainty Principle
The uncertainty decreases as Δz increases and vice versa. It can be inferred that Δz Δpz ≥ h/2π*. If the position of a particle is known with any precision, the simultaneous determination of its velocity will be imprecise, i.e., the value of the velocity would not be known, and vice versa.
Radioactive Emissions
Nuclei formed by alpha particles (helium-4 nuclei) have a classical velocity between 5% and 7.5% of the speed of light in a vacuum. Beta particles are formed by electrons with a velocity that can exceed 90% of the speed of light. Gamma radiation is electromagnetic radiation and therefore propagates at the speed of light; its wavelength λ < 10-10m is less than that of X-rays.
Radioactive Decay
Radioactive decay is a spontaneous process that takes place completely randomly and is not influenced by external agents. It does not depend on the state of aggregation or subdivision of the sample, or whether it is free or forming compounds. A = dN / dt (absolute value) = λ N, where A is the activity, N is the number of radioactive nuclei, and λ* is the decay constant.
Half-Life
Half-life is the time it takes for half of the atoms in a sample of a radioactive isotope to decay (t1/2). t1/2 = ln(2) / λ.
Nuclear Fission
Nuclear fission is a process in which a heavy nucleus generally breaks into two lighter fragments. It takes place with a loss of mass and is very exoenergetic, with neutrons being released.
Nuclear Fusion
Nuclear fusion is a process in which two or more light nuclei combine to form a heavier nucleus and one or more particles or gamma radiation. In this process, the mass decreases, and an equivalent amount of energy appears. The elements used are widespread in nature. It is a clean process, with minimal radioactive waste generation.