Magnetic quantum number - wikipedia Magnetic quantum number This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. ( May 2016 ) In atomic physics, the magnetic quantum number, designated by the letter m, is the third in a set of four quantum numbers ( the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number ) which describe the unique quantum state of an electron. The magnetic quantum number distinguishes the orbitals available within a subshell, and is used to calculate the azimuthal component of the orientation of orbital in space. Electrons in a particular subshell ( such as s, p, d, or f ) are defined by values of l ( 0, 1, 2, or 3 ). The value of m can range from - l to + l, inclusive of zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each, with values of m within the ranges 0, ± 1, ± 2, ± 3 respectively. Each of these orbitals can accommodate up to two electrons ( with opposite spins ), forming the basis of the periodic table. Contents 1 Derivation 2 As a component of angular momentum 3 Effect in magnetic fields 4 See also 5 References Derivation Relative to the up - down axis, these f orbitals either show no azimuthal dependence ( m = 0 ) or symmetry under 360 degree, 180 degree, and 120 degree rotations ( m = 1, 2, 3, respectively ). This reflects the e m i φ ( displaystyle e ^ ( mi phi ) ) dependence of the azimuthal component. There is a set of quantum numbers associated with the energy states of the atom. The four quantum numbers n ( displaystyle n ), l ( displaystyle ell ), m ( displaystyle m ), and s ( displaystyle s ) specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The Schrodinger equation for the wavefunction of an atom with one electron is a separable partial differential equation. ( This is not the case for the helium atom or other atoms with mutually interacting electrons, which require more sophisticated methods for solution ) This means that the wavefunction as expressed in spherical coordinates can be broken down into the product of three functions of the radius, colatitude ( or polar ) angle, and azimuth : ψ ( r, θ, φ ) = R ( r ) P ( θ ) F ( φ ) ( displaystyle psi ( r, \theta, phi ) = R ( r ) P ( \theta ) F ( phi ) ) The differential equation for F ( displaystyle F ) can be solved in the form F ( φ ) = A e λ φ ( displaystyle F ( phi ) = Ae ^ ( lambda phi ) ). Because values of the azimuth angle φ ( displaystyle phi ) differing by 2 π ( displaystyle pi ) ( 360 degrees in radians ) represent the same position in space, and the overall magnitude of F ( displaystyle F ) does not grow with arbitrarily large φ ( displaystyle phi ) as it would for a real exponent, the coefficient λ ( displaystyle lambda ) must be quantized to integer multiples of i ( displaystyle i ), producing an imaginary exponent : λ = i m ( displaystyle lambda = im ). These integers are the magnetic quantum numbers. The same constant appears in the colatitude equation, where larger values of m ( displaystyle m ) tend to decrease the magnitude of P ( θ ) ( displaystyle P ( \theta ) ), and values of m ( displaystyle m ) greater than the azimuthal quantum number l ( displaystyle ell ) do not permit any solution for P ( θ ) ( displaystyle P ( \theta ) ). Relationship between Quantum Numbers Orbital Values Number of Values for m ( displaystyle m ) Electrons per subshell s l = 0, m = 0 ( displaystyle ell = 0, quad m = 0 ) p l = 1, m = − 1, 0, + 1 ( displaystyle ell = 1, quad m = - 1, 0, + 1 ) 6 d l = 2, m = − 2, − 1, 0, + 1, + 2 ( displaystyle ell = 2, quad m = - 2, - 1, 0, + 1, + 2 ) 5 10 f l = 3, m = − 3, − 2, − 1, 0, + 1, + 2, + 3 ( displaystyle ell = 3, quad m = - 3, - 2, - 1, 0, + 1, + 2, + 3 ) 7 14 g l = 4, m = − 4, − 3, − 2, − 1, 0, + 1, + 2, + 3, + 4 ( displaystyle ell = 4, quad m = - 4, - 3, - 2, - 1, 0, + 1, + 2, + 3, + 4 ) 9 18 As a component of angular momentum Illustration of quantum mechanical orbital angular momentum. The cones and plane represent possible orientations of the angular momentum vector for l = 2 ( displaystyle ell = 2 ) and m = − 2, − 1, 0, 1, 2 ( displaystyle m = - 2, - 1, 0, 1, 2 ). Even for the extreme values of m ( displaystyle m ), the z component of this vector is less than its total magnitude. The axis used for the polar coordinates in this analysis is chosen arbitrarily. The quantum number m refers to the projection of the angular momentum in this arbitrarily chosen direction, conventionally called the z direction or quantization axis. L, the magnitude of the angular momentum in the z direction, is given by the formula : L z = m ħ. ( displaystyle L_ ( z ) = m hbar. ) This is a component of the atomic electron 's total angular momentum, L ( displaystyle mathbf ( L ) ), whose magnitude is related to the azimuthal quantum number of its subshell l ( displaystyle ell ) by the equation : L = ħ l ( l + 1 ) ( displaystyle L = hbar ( sqrt ( ell ( ell + 1 ) ) ) ) where ħ ( displaystyle hbar ) is the reduced Planck constant. Note this L = 0 ( displaystyle L = 0 ) for l = 0 ( displaystyle ell = 0 ) and approximates L = ( l + 0.5 ) ħ ( displaystyle L = ( ell + 0.5 ) hbar ) for high l ( displaystyle ell ). It is not possible to measure the angular momentum of the electron in all three axes simultaneously. These properties were first demonstrated in the Stern - Gerlach experiment, by Otto Stern and Walther Gerlach. The energy of any wave is the frequency multiplied by Planck 's constant. This causes the wave to display particle - like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck 's reduced constant which only allows particular or discrete or quantized energy levels. Effect in magnetic fields The quantum number m ( displaystyle m ) refers, loosely, to the direction of the angular momentum vector. The magnetic quantum number m ( displaystyle m ) only affects the electron 's energy if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of m ( displaystyle m ) are equivalent. The magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field ( the Zeeman effect ) -- hence the name magnetic quantum number. However, the actual magnetic dipole moment of an electron in an atomic orbital arrives not only from the electron angular momentum, but also from the electron spin, expressed in the spin quantum number. Since each electron has a magnetic moment in a magnetic field, it will be subject to a torque which tends to make the vector L ( displaystyle mathbf ( L ) ) parallel to the field, a phenomenon known as Larmor precession. See also Quantum number Azimuthal quantum number Principal quantum number Spin quantum number Total angular momentum quantum number Basic quantum mechanics Bohr atom Schrödinger equation References Jump up ^ `` Helium atom ''. 2010 - 07 - 20. Jump up ^ `` Hyperphysics : the hydrogen atom ''. Jump up ^ `` Hyperphysics : the azimuthal equation ''. ^ Jump up to : Herzberg, Gerhard ( 1950 ). Molecular Spectra and Molecular Structure ( 2 ed. ). D van Nostrand Company. pp. 17 -- 18. Jump up ^ `` Spectroscopy : angular momentum quantum number ''. Encyclopædia Britannica. Electron configuration Introduction to quantum mechanics Quantum mechanics Quantum numbers Principal quantum number ( n ) Azimuthal quantum number ( l ) Magnetic quantum number ( m ) Spin quantum number ( s ) Periodic table Periodic table ( electron configurations ) Others Pauli exclusion principle Hund 's rule Octet rule Aufbau principle Retrieved from `` https://en.wikipedia.org/w/index.php?title=Magnetic_quantum_number&oldid=807038839 '' Categories : Atomic physics Rotational symmetry Quantum numbers Hidden categories : Articles needing additional references from May 2016 All articles needing additional references All accuracy disputes Articles with disputed statements from May 2016 Talk Contents About Wikipedia Čeština Ελληνικά Español فارسی Français 한국어 Bahasa Indonesia Italiano עברית Македонски Polski Português Română Русский Slovenščina Suomi Svenska Татарча / tatarça Українська Tiếng Việt 中文 Edit links This page was last edited on 25 October 2017, at 14 : 18. 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Question: the orientation in space is represented by which quantum number
Answer: magnetic