Principal quantum number in the context of "Balmer series"

In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m_ℓ, the magnetic quantum number; and m_s, the spin quantum number. For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m_ℓ are equal. In that case, the two values of m_s (spin) pair must be different. Since the only two possible values for the spin projection m_s are +1/2 and −1/2, it follows that one electron must have m_s = +1/2 and one m_s = −1/2.

In atomic physics, the Bohr model or Rutherford–Bohr model is an obsolete model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's discover of the atom's nucleus, it supplanted the plum pudding model of J. J. Thomson only to be replaced by the quantum atomic model in the 1920s. It consists of a small, dense atomic nucleus surrounded by orbiting electrons. It is analogous to the structure of the Solar System, but with attraction provided by electrostatic force rather than gravity, and with the electron energies quantized (assuming only discrete values).

In the history of atomic physics, it followed, and ultimately replaced, several earlier models, including Joseph Larmor's Solar System model (1897), Jean Perrin's model (1901), the cubical model (1902), Hantaro Nagaoka's Saturnian model (1904), the plum pudding model (1904), Arthur Haas's quantum model (1910), the Rutherford model (1911), and John William Nicholson's nuclear quantum model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum mechanical interpretation introduced by Haas and Nicholson, but forsaking any attempt to explain radiation according to classical physics.

In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_ℓ, and the spin quantum number m_s).

For a given value of the principal quantum number n (electron shell), the possible values of ℓ are the integers from 0 to n − 1. For instance, the n = 1 shell has only orbitals with ${\displaystyle \ell =0}$, and the n = 2 shell has only orbitals with ${\displaystyle \ell =0}$, and ${\displaystyle \ell =1}$.

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.

In chemistry and atomic physics, an electron shell, or principal energy level, may be thought of as the orbit of one or more electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on further and further from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4, ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, N, ...).

In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantum numbers includes the principal, azimuthal, magnetic, and spin quantum numbers. To describe other systems, different quantum numbers are required. For subatomic particles, one needs to introduce new quantum numbers, such as the flavour of quarks, which have no classical correspondence.

Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian of the system, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics.

In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (m_l or m) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the z-axis, so it describes the orientation of the orbital in space. The spin magnetic quantum number m_s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1⁄2, and m_s is either +1⁄2 or −1⁄2, often called "spin-up" and "spin-down", or α and β. The term magnetic in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the Zeeman effect.

The four quantum numbers conventionally used to describe the quantum state of an electron in an atom are the principal quantum number n, the azimuthal (orbital) quantum number ${\displaystyle \ell }$, and the magnetic quantum numbers m_l and m_s. Electrons in a given subshell of an atom (such as s, p, d, or f) are defined by values of ${\displaystyle \ell }$ (0, 1, 2, or 3). The orbital magnetic quantum number takes integer values in the range from ${\displaystyle -\ell }$ to ${\displaystyle +\ell }$, including zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each. Each of these orbitals can accommodate up to two electrons (with opposite spins), forming the basis of the periodic table.

In chemistry and atomic physics, an electron shell may be thought of as an orbit that electrons follow around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on further and further from the nucleus. The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, ...). Each period on the conventional periodic table of elements represents an electron shell.

Each shell can contain only a fixed number of electrons: the first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18, continuing as the general formula of the nth shell being able to hold up to 2(n) electrons. For an explanation of why electrons exist in these shells, see electron configuration.

The hydrogen line, 21 centimeter line, or H I line is a spectral line that is created by a change in the energy state of solitary, electrically neutral hydrogen atoms. It is produced by a spin-flip transition, which means the direction of the electron's spin is reversed relative to the spin of the proton. This is a quantum state change between the two hyperfine levels of the hydrogen 1 s ground state. The electromagnetic radiation producing this line has a frequency of 1420.405751768(2) MHz (1.42 GHz), which is equivalent to a wavelength of 21.106114054160(30) cm in a vacuum. According to the Planck–Einstein relation E = hν, the photon emitted by this transition has an energy of 5.8743261841116(81) μeV [9.411708152678(13)×10 J]. The constant of proportionality, h, is known as the Planck constant.

The hydrogen line frequency lies in the L band, which is located in the lower end of the microwave region of the electromagnetic spectrum. It is frequently observed in radio astronomy because those radio waves can penetrate the large clouds of interstellar cosmic dust that are opaque to visible light. The existence of this line was predicted by Dutch astronomer H. van de Hulst in 1944, then directly observed by E. M. Purcell and his student H. I. Ewen in 1951. Observations of the hydrogen line have been used to reveal the spiral shape of the Milky Way, to calculate the mass and dynamics of individual galaxies, and to test for changes to the fine-structure constant over time. It is of particular importance to cosmology because it can be used to study the early Universe. Due to its fundamental properties, this line is of interest in the search for extraterrestrial intelligence. This line is the theoretical basis of the hydrogen maser.