Quantum Mechanics Flashcards
Quantum Mechanics
A system of mechanics that was developed from *quantum theory and is used to explain the properties of atoms and molecules. Using the energy *quantum as a starting point it incorporates Heisenberg’s *uncertainty principle and the *de Broglie wavelength to establish the wave-particle duality on which the *Schrödinger equation is based. This form of quantum mechanics is called *wave mechanics.
Bohr’s atom
An atom that can be explained using Bohr’s Theory. Only atoms with only one electron can be used to explain his theory. Ex: hydrogen, He⁺, Li²⁺, etc.
Quantum model
A model of the atom that applies principles of the quantum theory and/or wave-particle duality
line spectrum
Line spectra are discontinuous lines produced by excited atoms and ions as they fall back to a lower energy level.
Wave-Particle duality
The concept that waves carrying energy may have a corpuscular aspect and that particles may have a wave aspect; which of the two models is the more appropriate will depend on the properties the model is seeking to explain. For example, waves of electromagnetic radiation need to be visualized as particles, called *photons, to explain the photoelectric effect while electrons need to be thought of as de Broglie waves in *electron diffraction.
Louis de Broglie
He is best known for his 1923 theory of wave– particle duality, which postulated that particles such as *electrons can sometimes also be regarded as waves. This proved important in quantum theory.
de Broglie Wavelength
The wavelength of the wave associated with a moving particle. The wavelength (λ) is given by λ = h / mv , where h is the Planck constant, m is the mass of the particle, and v its velocity. The de Broglie wave was first suggested by Louis de Broglie in 1923 on the grounds that since electromagnetic waves can be treated as particles (photons) one could therefore expect particles to behave in some circumstances like waves.
Heinsberg’s Uncertainty Principle
The principle that it is not possible to know with unlimited accuracy both the position and momentum of a particle. This principle, discovered in 1927 by Werner *Heisenberg, is usually stated in the form: Δ x Δ p x ≥ h /4π, where Δ x is the uncertainty in the x -coordinate of the particle, Δ p x is the uncertainty in the x -component of the particle’s momentum, and h is the *Planck constant.
wavefunction
wave function A function ψ( r , θ , ϕ OR x , y, z) appearing in the *Schrödinger equation in wave mechanics. The wave function is a mathematical expression involving the coordinates of a particle in space. The physical significance of the wave function is that the square of its absolute value, |ψ| ² , at a point is proportional to the probability of finding the particle in a small element of volume, d x d y d z , at that point. For an electron in an atom, this gives rise to the idea of atomic and molecular *orbitals.
Orbital
A region in which an electron may be found in an atom or molecule. According to *wave mechanics, the electron has a certain probability of being in a given element of space. The probabilities of finding an electron in different regions can be obtained by solving the Schrödinger wave equation to give the wave function ψ, and the probability of location per unit volume is then proportional to |ψ| ² .
AKA the region in the atom where there is the highest probability of finding the atom.
Probability density
|ψ| ² , the probability of finding an e⁻⁻ in a given space belonging to the atom
the set of quantum numbers
n, 𝓁, m𝓁, ms
n
The principal quantum number n gives the main energy level and has values 1, 2, 3, etc. (the higher the number, the further on average the electron from the nucleus). Traditionally, these levels, or the orbits corresponding to them, are referred to as shells. The maximum number of electrons in a given shell is 2 n².
𝓁
The orbital quantum number 𝓁 , which governs the angular momentum of the electron. The possible values of 𝓁 are 0 to (n-1). Thus, in the first shell ( n = 1) the electrons can only have angular momentum zero ( 𝓁 = 0). In the second shell ( n = 2), the values of 𝓁 can be 1 or 0, giving rise to two subshells of slightly different energy. In the third shell ( n = 3) there are three subshells, with 𝓁 = 2, 1, or 0. The subshells are denoted by letters s ( 𝓁 = 0) (AKA the s-orbital) , p ( 𝓁 = 1), d ( 𝓁 = 2), f ( 𝓁 = 3). The number of electrons in each subshell is written as a superscript numeral to the subshell symbol, and the maximum number of electrons in each subshell is s 2 , p 6 , d 10 , and f 14 .
m𝓁
The magnetic quantum number m𝓁 , which governs the energies of electrons in an external magnetic field and refers to the 3D orientation of the orbitals around the nucleus. This can take values of + 𝓁 to – 𝓁 . In an s -subshell (i.e. 𝓁 = 0) the value of m = 0. In a p -subshell ( 𝓁 = 1), m can have values +1, 0, and –1; i.e. there are three p -orbitals in the p -subshell, usually designated p x , p y , and p z . Under normal circumstances, these all have the same energy level.
ms
The spin quantum number ms , which gives the spin of the individual electrons and can have the values +½ or –½. Refers to the upward or downward spin.
