Atomic Structure and Quantum Theory

Posted on Oct 10, 2024 in Physics

ATOMIC PARAMETERS

Atomic Number and Mass Number

Each atom is defined by two features: its atomic number and mass number.

  • The atomic number indicates the number of protons in the nucleus and determines the element in question. It is represented by the letter Z.
  • The mass number is the number of nucleons (neutrons and protons) that make up the nucleus and determines the isotope of the element. It is represented by the letter A.

Isotope notation includes the mass number (A), atomic number (Z), and the element symbol (X), as follows: AZX

Atomic Mass vs. Isotope Mass

Do not confuse the atomic mass of an element with the mass of each isotope of an atom.

  • If we find the mass (in atomic mass units) of a particular atom of an element, we get only the isotope mass corresponding to the chosen isotope.
  • The atomic mass of an element represents the average of the isotopic masses of its naturally occurring isotopes.

Origins of Quantum Theory

In the mid-nineteenth century, Scottish physicist and mathematician James C. Maxwell developed the classical theory of electromagnetism, which explained light based on everything known at the time.

However, in the early twentieth century, experimental results forced the development of new theories about light. These theories initially focused on the energy carried by light and were subsequently used to develop new atomic theories.

According to Maxwell’s theory, light is an electromagnetic wave with specific characteristics.

Atomic Emission Spectra

All substances absorb, emit, or reflect energy. The emission spectrum of an element is the radiation it emits in gaseous form when provided with sufficient energy. Sunlight’s spectrum is continuous, meaning it contains radiation of all frequencies.

In contrast, the emission spectra of elements are discontinuous. Elements in a gaseous state only emit radiation at specific frequencies. A chemical element always emits the same spectrum, and no two elements have the same emission spectrum. Therefore, the emission spectrum can be considered the fingerprint of an element.

Planck’s Quantum Theory

According to the classical theory of electromagnetism, the energy of a wave depends only on its amplitude. However, when applying this theory to the radiation emitted by a body at a given temperature, the theoretical results differed significantly from experimental observations.

In 1900, German physicist Max Planck (1858-1947) proposed a revolutionary theory that explained the experimental results: the quantum theory.

Planck’s theory states that bodies emit or absorb energy in the form of discrete packets or quanta.

Photoelectric Effect

In 1887, German physicist Heinrich Hertz discovered that when electromagnetic radiation strikes a metal surface, it emits electrons. This phenomenon is called the photoelectric effect.

Characteristics of the Photoelectric Effect

  • The photoelectric effect occurs only if the frequency of the radiation exceeds a certain frequency called the cutoff frequency (v0). The value of v0 depends on the metal used.
  • The emitted electrons have kinetic energy that increases with increasing radiation frequency.
  • Increasing the radiation intensity does not change the energy of the emitted electrons but increases their number per unit time.

Albert Einstein (1879-1955) explained this effect in 1905 using quantum theory. He considered that electromagnetic radiation consists of energy quanta, which he called photons.

When a photon of frequency v and energy hv is incident on a metal surface, it transfers its energy to an electron. The electron uses part of this energy (W = hv0) to escape the metal, and the rest is used to increase its kinetic energy.

Limitations of the Rutherford Atomic Model

Although the atomic model proposed by Rutherford was a major advance in understanding the atom, it had some limitations:

  • In Rutherford’s model, electrons move in circular orbits and therefore have normal acceleration. According to the principles of classical electromagnetism, an accelerating electric charge should emit energy. Therefore, the electrons would spiral into the nucleus and collide with it. Meanwhile, the atom would lose energy in the form of electromagnetic radiation with a continuous spectrum.
  • The electron would pass through all possible orbits, describing a spiral centered on the atomic nucleus, and therefore the radiation should be continuous. However, the atomic emission spectra of elements are discontinuous.

Bohr Model

Since the advent of the Rutherford model, it was clear that the atom consists of a nucleus and an electron cloud.

The next step in determining the atomic structure was taken by Danish physicist Niels Bohr (1885-1962), who applied new ideas about the quantization of energy to the hydrogen atom. This allowed him to explain the discontinuous emission spectrum.

In 1913, Bohr developed a new atomic model based on the following postulates:

  • The energy of the electron inside the atom is quantized. This means that the electron occupies specific positions or stationary states around the nucleus with certain energy values.
  • The electron moves in circular orbits around the nucleus. Each of these orbits is a stationary state or allowed energy level and is associated with a natural number, n: 1, 2, 3…
  • The allowed energy levels of the electron are those for which its angular momentum, mvr (m: mass, v: electron velocity, r: radius of the orbit), is a multiple of h/2π, where h is Planck’s constant.
  • Energy is absorbed or emitted only when an electron moves from one energy level to another. If we call Ei the initial energy level and Ef the final energy level, the corresponding energy change (ΔE) and its frequency (v) will be: ΔE = Ef – Ei = hv