# Physical Chemistry 2 Exam 1 UTC

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blackbody

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A blackbody is an idealized object that emits and absorbs all frequencies. A true blackbody does not exist, but a close approximation can be made for labs.

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blackbody radiation

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Blackbody radiation is the emission of radiation from a black body. Its study led to the development of quantum mechanics due to classical physics’ failure to explain it properly. It was improperly described by the Raleigh Jeans law, properly described by Max Planck.

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Wien displacement law (give f)

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The Wein displacement law is the relationship between the wavelength at the maximum intensity and the temperature. They are indirectly proportional.

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ultraviolet catastrophe

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Ultraviolet catastrophe represents the classical interpretation of the blackbody radiation that predicted emitted radiation of large intensities in the UV region; property that is not experimentally observed.

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Planck constant

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The Planck constant is h. It is the constant that relates frequency to energy in E=hnu and pops up all over quantum mechanics. The units imply action. Discovered by Max Planck.

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photoelectrons

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are electrons emitted during the photoelectric effect due to a photon of light hitting a surface with the required threshold frequency.

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photon

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a photon is a small packet (quanta) of energy the form of electromagnetic radiation.

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threshold frequency

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The property of metallic surfaces to emit electron upon irradiation is called the photoelectric effect. The threshold frequency (0) is a limit of the radiation frequency below which the photoelectric effect is not observed. The threshold frequency is related to the work function by: = hnu_o

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work function

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The property of metallic surfaces to emit electron upon irradiation is called the photoelectric effect. The minimum energy required to remove an electron from the surface of a particular metal is the work function

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line spectra

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is the emission spectra of an atom showing isolated lines at specific discrete frequencies and can be used as a fingerprint for the element.

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Lyman, Balmer, Pashen, Bracket series

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The Lyman series is UV. goes to n =1 The Balmer series is a series of lines in the spectrum of H atom, corresponding to transitions from n = 3,4,5,… to n = 2. This series of lines appear mostly in the visible range of radiation. The Pashen series is mostly in the near infrared region. goes to n = 3 The Bracket series is the infrared region. goes to n=4.

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series limit

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The series limit is the frequency that is converged on by line spectra in a seires. It is the result of the energy being emitted by returning to a lower energy level (n1) from a higher energy level (n2). The limit is reached as n2 approaches infinity.

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Balmer formula

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describes the balmer series, the emission spectrum of hyrogen in visible region

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Rydberg formula

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A general equation for the emission line spectra of hydrogen. It uses the rydberg constant, orginally found experimentally, looks at transitions from higher energy states to lower energy states.

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term

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Rydberg constant

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The rydberg constant is originally determined experimentally by Rydberg, but was later derived from serveral other constants in the Bohr Model.

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angular momentum

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the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity.

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stationary state or orbit

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is the location and path of the bohr model of hydrogen at discrite positions. It is required so that the electron does not accelarate into the nucleus due to Columbic charges.

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first Bohr radius

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is the smallest allowed radius of an electron’s orbit in the Bohr model.

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ground state

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is the lowest level the electron can occupy. In a system for the bohr model it is n=1, while for the harmonic oscillator it is n=0. States other than the ground state are called excited states.

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excited states

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Excited states are states of higher energy than the ground state.

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Bohr frequency condition

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is that the frequency of the electron during a transition from one electron state to another is related to the change in energy. DeltaE=hnu

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wave-particle duality

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is the phenomena that light and all of matter acts both like a wave and like a particle to a certain degree, depending on mass, velocity, and plancks constant

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de Broglie wavelength

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The movement of any particle has some wavelike character, and the de Broglie wavelength is the wavelength associated with the moving particle. This wavelength is given by

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Heisenberg Uncertainty Principle

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Two properties for which the operators do not commute (like the position and the momentum or the energy and time) cannot be known (or measured) simultaneously with any arbitrary precision.

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SchrÃ¶dinger equation

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The schrodinger equation is the equation for finding the wavefunction of a particle, and is based on the idea of wave-particle duality. It can be written as time-independent or time-dependent, and its solutions are called stationary state wavefunctions. It can be simplified to GIVE using operators.

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wavefunctions

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A wavefunction psi is a solution of the SchrÃ¶dinger equation for a particular system. The most important property of the wavefunction if that psi*psi dx gives the probability of finding the particle at a certain position.

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operator

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an operator is a symbol that tells you to do something to whatever follows the symbol.

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operand

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is the quantity that an operation is performed on, as dictated by the operator.

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Laplacian operator

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A operator that signifies that the second partial derivative should be taken to x, y, and z.

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Hamiltonian operator

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The Hamiltonian operator is the operator for total energy, and is the sum of the operator for kinetic energy and the operator for the potential energy: The Hamiltonian eigenvalue is the total energy. A node is a geometric location (point, line, surface, etc.) where the wavefunction (or the amplitude of the wave) is zero.

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eigenvalue-eigenfunction relation

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An eigenfunction is a function that is retained after an operation is performed on it, dictated by the operator. The eigenvalue is a constant that is multiplied against the eigenfunction after the operation. A^*phi=alpha*phi

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complex conjugate

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the complex conjugate of the wavefunction is obtained by replacing i with -i in the expression of the wavefunction. Multiplying psi*psi gives a real product.

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QM postulates

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wavefunction interpretation

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Hermitian operator

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a hermitian operator is a linear operator that exists in quantum mechanics for every observable in classic physics An operator is hermitian if it is linear and if the integral over psi1*A^psi2 = integral over psi2(A^psi1)

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observable

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is a measurable dynamic value such as energy, position, momentum, etc

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average value

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normalized/normalizable

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A wavefunction being normalized is a condition that must be satisfied to properly represent the probability of finding the particle. It means that the integral over the wavefunction times its complex conjugate must be one. Normalizable – ?

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commutation

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Is a property of operators in which A^B^f(x) = B^A^f(x). Operators generally do not commute.

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commutator

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is [A^,B^] = A^B^-B^A^ The commutator of commuting operators is the zero operator.

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linear operators

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an operator is linear if it is distributive over two functions and their constants

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variance/standard deviation

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The varience is the square of the standard deviaton The standard deviation is a representation of the uncertainty in a measurement, whether two uncertainties they can both be determined with arbitrary precision is related to their product and the commutator.

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orthogonal

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If integral of (psi^*_i)(psi_j) is zero

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orthonormal

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If integral of (psi^*_i)(psi_j) is one and i = j

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even function

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An even function is a function for which f(x) = f(-x). An even function is always orthogonal to an odd function over an interval centered at 0.

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odd function

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â–¡ An odd function is a function for which f(x) = -f(-x). An even function is always orthogonal to an odd function over an interval centered at 0.

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complete set

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complete set of commuting observables (CSCO) is a set of commuting operators whose eigenvalues completely specify the state of a system.[1] ‘set from which all elements of our space can be constructed by linear combination

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particle-in-a-box

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The particle-in-a-box refers to the quantum mechanical treatment of translational motion. b. One tries to solve the SchrÃ¶dinger equationto obtain the wavefunctions and the allowed energies for the particle

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normalization constant

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allows the function to be normalized

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probability density

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probability that particle is located in that region orbital uses, what is typically represented is the boundary surface of the orbital, which is the surface (of equal electron density) that contains 90% of electron density.

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free-electron model

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model of valence electrons in a crystalline metallic solid

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Correspondence Principle

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Quantum mechanics results and classical mechanics results tend to agree in the limit of large quantum numbers. The large-quantum-number limit is called the classical limit.

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classical limit

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This is an illustration of the Correspondence Principle that says that quantum mechanics results and classical mechanics results tend to agree in the limit of large quantum numbers. â–¡ The large-quantum-number limit is called the classical limit.

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separable Hamiltonian

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separating the hamiltonian into different dimensions

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harmonic oscillator

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The harmonic oscillator refers to the quantum mechanical treatment of vibrational motion The quantum-mechanical harmonic oscillator model accounts for the IR spectrum of a diatomic molecule.

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reduced mass

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The movement of a two-body system can be replaced by the movement of a one-body system where the mass is replaced with the reduced mass

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Hermite polynomials

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polynomial functions used in harmonic oscillator wavefunctions

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zero-point energy

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Is the residual energy of the harmonic oscillator, it is different (i.e., bigger) than zero, and it is obtained for vibrational quantum number n = 0

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selection rule

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The transitions between various levels in harmonic oscillator model follow the selection rule:

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vibration

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fundamental vibrational frequency

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The quantum-mechanical harmonic oscillator predicts the existence of only one frequency in the spectrum of a diatomic, the frequency called fundamental vibrational frequecy

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tunneling

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The quantum mechanical particles have the property of non-zero probability in regions forbidden by classical mechanics.

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rigid rotator

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The rigid rotator (or rigid rotor) refers to the quantum mechanical treatment of rotational motion. b. The quantum mechanical rigid rotator is a model for a rotating diatomic molecule.

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moment of inertia

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analague to mass in rotational motion

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spherical harmonic functions

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angular portion of wavefunction, rigid rotor wavefunctions

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degeneracy

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Degeneracy represents the property of two or more eigenfunctions (or wavefunctions) having the same eigenvalue. The energy is one possible such eigenvalue.

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microwave spectroscopy

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transitions between energy states of rotational motion, rigid rotor model

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rotational constant

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write the frequency in terms of the rotational constant B

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spherical coordinates

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r, phi, theta

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angular momentum

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analogue to linear momentum, inertia times angular velocity

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atomic orbitals

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term used to represent the wavefunctions are that depend on 3 quantum numbers, the boundary surface, or the probability density

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Legendre polynomials

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the P stuff in HAM model angular wavefunctions

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angular momentum magnitude

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L=hbar sqrt(L(L+1)

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associated Laguerre polynomials

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polynomials for radial hydrogen wavefunctions

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boundary surface

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the boundary surface of the orbital, which is the surface (of equal electron density) that contains 90% of electron density.

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most probable value of r

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most probable radius of 1s orbital is the first bohr radius

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principal quantum number

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The principal quantum number n: a. Can take values of n = 1,2,… b. It describes the shell or level.

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azimuthal/secondary/orbital quantum number

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The angular momentum quantum number l: a. It is also called azimuthal or secondary or orbital quantum number. b. Can take values between 0 and n-1: l = 0,1,…,n-1 c. It describes the type of subshell (or shape of orbital), and, in addition to n, the actual subshell or sublevel. determined angular momentum

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magnetic quantum number

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he magnetic quantum number m: a. More specifically denoted m l as we will see later. b. It can take (2l + 1) values: l m ,…, 2 , 1 , 0 â–¡ Same as the degeneracy of the l sublevel or subshell. c. It describes the orientation (or type) of orbitals, and, in addition to n and l, the actual orbital. d. Quantum number m completely determine the z component of the angular momentum (L z ): m L z e. The quantum number m is called magnetic because the energy of hydrogen atom in a magnetic field depends on m.

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Separation of Variables

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It is a technique of solving multivariable equations. In particular, solving Schrodinger equation by writing the Hamiltonian as a sum of terms leads to the overall wavefunction to be the product of functions

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Zeeman effect

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Each energy level has a degeneracy of (2l + 1) which is removed in magnetic field. â–¡ This is knows as the Zeeman e