Hydrogen Energy Levels
First of all, the atom is the smallest unit of structure with physical and chemical properties of matter. With the emergence of the modern atomic concept and the newly developed theories, our thoughts on the nature of the atom have developed and replaced by new and unified theories.
Even though the current one known and accepted today is Quantum Atom Theory, we can foresee that it will evolve and leave its place to more extensive theories. However, since today’s atom theories are developed based on the Bohr Atom Model, we will refer to the Bohr Atom Model and the Bohr Model of the hydrogen atom.
Structure of Atom
The diameter of an atom is approximately 10ˉ¹⁰. A large portion of the mass of the atom forms an atomic nucleus with a diameter of about 10ˉ¹⁴ meters. Although the core is small in volume, it comprises most of the atom’s mass. The atomic nucleus has two particles. These are protons and neutrons.
Protons are positively charged particles that balance the charge of electrons. The number of protons is the distinguishing feature for atoms.
Neutrons are neutral particles without charge. It is heavier than the proton also their number change according to the type of atoms. Electrons move in orbits outside of the nucleus and are the particles whose number can vary in chemical reactions. We can’t rightly say these particle’s exact location.
Nevertheless, we can define quantum mechanics according to the probability of finding electrons in particular trajectories. Still, this possibility concept was not carried out by the Bohr Atomic Model, but in 1926, when Erwin Schrödinger took the Bohr Atomic Model a step further and moved to atomic models.
Atomic number = Number of Protons
Mass Number = Number of Protons + Number of Neutrons
Ionic charge = Number of Protons – Number of Electrons
Bohr Model of Hydrogen Atom
Bohr’s Atomic Model + Ze defines a single electron that spins around a nucleus that is loaded and resembles the star systems in nature with the electrons rotating around the core. In 1913, Niels Bohr proposed the Bohr theory using the spectrum lines of the hydrogen atom and Planck’s quantum theory.
Bohr Atomic Theory
- The angular momentum of the electrons in these orbits must be in the form of multiples of h / 2π.
- Some can only find electrons at specific locations called “trajectories.”
- The photon (radiation) does not emit while the electron is in a steady state.
- Each specific position of the electron corresponds to certain amounts of energy level.
- Energy levels are discontinuous. The orbit number is also known as the head quantum number, and we denote it by n. It can take integer values such as n = 1,2,3,4…
- Bohr’s atomic model assumes that orbitals are in the form of circular orbits. However, this is not enough to fully explain the position of the electron. Because we can determine orbitals by two parameters such as energy and the angular momentum of the electron.
The Bohr Atom Model is still a useful model if we are only interested in energy.
The lowest energy level is referred to as the “ground state” and corresponds to the innermost n = 1 trajectory in the energy diagram. If the electron is at n = 1 energy level, we say that the atom is at its base level. Moreover, if the electron particle is located at an energy level higher than n = 1, namely n> 1, we call it an excited atom.
Shift Between Energy Levels
An atom needs to absorb enough energy to be stimulated and to reach the energy level to make in the quantum jump. It must be able to provide E= En – E₁ energy level.
There has to be enough energy to switch to at least the next energy level. The amounts of energy less than that cannot be absorbed or stored.
The energy for atom excitation can be derived from the reaction of the photons or through atomic collisions. The atom must unload energy, and the atom energy must be released in batch to get an excited atom. Atoms, stimulated by a photon release, tends to move back to a lower energy level.
Absorption of a Photon
You remember that the energy of a photon is E = hf. The f represents the frequency, and h represents the Planck constant.
Planck constant h= 6.626*10ˉ34J.s
If the frequency of the photon has an f= (En – E₁) / h frequency value, transitions from the base level are allowed.
If the atom is already stimulated and in the N. level and it is for the transition to the ‘n’ level;
It must be have a f = (En – EN) / h frequency.
Scientists call this process “absorption” because the atom is absorbing a photon. Furthermore, only photons with specific frequencies can be absorbed.
Emission of a Photon
We call photon emission to the vice-versa of the above situation. The transition of a high energy photon to a lower energy level is called photon emission. If the electron is n photon when switching from energy level to base level, it is emission with f = (En – E₁) frequency.
When the white light passes through the prism, according to the wavelengths, it breaks into its components. We call this process the spectrum of visible light. When there is no definite boundary between colours, a continuous range occurs.
If the beam emitted from an atom passes through a prism, we obtain a discrete spectrum or line spectrum. We categorize the discrete spectrum in two: emission and absorption spectrum.
The spectrum of Hydrogen Atom
Chemical elements determine the number of protons in the nucleus. The hydrogen atom consisting of 1 electron and 1 proton is crucial in the development of atomic structure due to its simple structure, light absorption, and emission spectrum. When the atom is not in the ionized state, the number of electrons is equal to the number of protons.
The energy of hydrogen can formulize like this: En = -R (Z² / n²).
Where n is the quantum number, R represents the Rydberg constant (R = 1.0973731568525 * 10⁷m25 = 13.6056923 eV), and Z represents the atomic number (number of protons).
Since Z = 1 for the hydrogen atom, E = -13.6 eV.
(1 eV= 1.60218*10ˉ¹⁹ Joule)
Scientists observed that the atom was only sensitive to certain wavelengths in the stimulation and photon release stages. Rydberg developed a formula in 1888; “1 / λ = R (1 / n1² -1 / n2²)“, thanks to the formula, we can characterize the transitions between the energy levels.
- Lyman Series for n1 = 1 (λ = 91.13 nm)
- Balmer Series for n1 = 2 (λ = 364.51 nm)
- Paschen Series for n1 = 3 (λ = 820.14 nm)
- Brackett Series for n1 = 4 (λ = 1458.03 nm)
- Pfund Series for n1 = 5 (λ = 2278.17 nm)
- Humphreys Series for n1 = 6 (λ = 3280.56 nm)
(λ indicates the shortest wavelength.)
Ionization and Reintegration(Recombination)
If the atom loads with too much energy, one or more electrons can move away from the atom, we call this process ionization. The process is different depending on whether the produced ion is plus or minus. For a charged ion, the electron in the atom must absorb enough energy from the external source to get rid of the electrical stress that restricts it.
As for a minus charged ion, an electron must collide with the atom and have to undergo electrical pressure. Considering the infinite level transition of an atom, the minimum energy required is called the ionization energy. The ionization energy at the base level for hydrogen is 13.6 eV.
If atoms are in a warm environment, they are ionized by colliding with each other. This process of contrast to the electron capture of the ion is called the process of reintegration.