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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 phrase spin quantum number refers to quantized spin angular momentum. The symbol s is used for the spin quantum number, and m s is described as the spin magnetic quantum number [3] or as the z-component of spin s z. [4] Both the total spin and the z-component of spin are quantized, leading to two quantum numbers spin and spin magnet quantum ...
2.5 Hydrogen atom. 3 See also. 4 Footnotes. ... m j = total angular momentum magnetic quantum number; Spin: ... m e = electron rest mass;
For hydrogen-1, hydrogen-2 , and hydrogen-3 which have finite mass, the constant must be slightly modified to use the reduced mass of the system, rather than simply the mass of the electron. This includes the kinetic energy of the nucleus in the problem, because the total (electron plus nuclear) kinetic energy is equivalent to the kinetic ...
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 ...
The integer m (not to be confused with the moment, ) is called the magnetic quantum number or the equatorial quantum number, which can take on any of 2j + 1 values: [20], (), , , , +, , + (), + . Due to the angular momentum, the dynamics of a magnetic dipole in a magnetic field differs from that of an electric dipole in an electric field.
The total magnetic moment , as a vector operator, does not lie on the direction of total angular momentum = +, because the g-factors for orbital and spin part are different. However, due to Wigner-Eckart theorem , its expectation value does effectively lie on the direction of J → {\displaystyle {\vec {J}}} which can be employed in the ...
The Bohr model explains the atomic spectrum of hydrogen (see Hydrogen spectral series) as well as various other atoms and ions. It is not perfectly accurate, but is a remarkably good approximation in many cases, and historically played an important role in the development of quantum mechanics. The Bohr model posits that electrons revolve around ...