* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Bohr`s equation for the hydrogen atom Bohr derived an equation to
Double-slit experiment wikipedia , lookup
Coherent states wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Renormalization group wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Quantum field theory wikipedia , lookup
Bell's theorem wikipedia , lookup
Quantum entanglement wikipedia , lookup
Matter wave wikipedia , lookup
Quantum fiction wikipedia , lookup
Quantum dot wikipedia , lookup
Renormalization wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Quantum computing wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Path integral formulation wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Quantum machine learning wikipedia , lookup
Quantum key distribution wikipedia , lookup
Quantum teleportation wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Quantum group wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
EPR paradox wikipedia , lookup
Particle in a box wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum state wikipedia , lookup
History of quantum field theory wikipedia , lookup
Wave–particle duality wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Hidden variable theory wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Atomic theory wikipedia , lookup
Bohr's equation for the hydrogen atom Bohr derived an equation to give the values of the energy levels in the hydrogen atom. Bohr showed that the energy levels were proportional to 1/n2, where n is an integer. When an electron falls from one energy level E2 to another level E1 radiation of frequency f will be emitted. Bohr showed that the energy difference (E2 - E1 = hf) was given by the equation: E2 - E1 = hf = me4/[8och3](1/n12 – 1/n22) Where n1 and n2 are integers (1, 2, 3. . .) and the other constants have their usual meanings. The equation can be expressed in the form of wave number (1/) as: 1/ = me4/[8och3](1/n12 – 1/n22) The term me4/[8och3] is known as Rydberg's constant (R). R = 1.097 x 107 m-1. Putting m = 1,2 or 3 will give us three series of energy changes and therefore three series of wavelengths: Therefore: n1 = 1 gives the Lyman series (ultraviolet); n1 = 2 gives the Balmer series (visible); n1 = 3 gives the Paschen series (infrared). Quantum numbers The full treatment of the electron energy in terms of quantum numbers is not predicted by the simple Bohr model. Every electron within an atom is considered to have four quantum numbers: (a) the principal quantum number (n), representing the energy level; (b) the orbital quantum number (L), which may have any integral value between 0 and n -1; (c) the magnetic quantum number (m), which may have any integral value between - L and +L (NB it is normal to write the orbital quantum number as l but we are using L to make it clearly different from1.) (d) the spin quantum number (s), which may have values of + ½ or – ½ . Related to these quantum numbers is the Pauli exclusion principle which states that no two electrons in an atom may exist in the same quantum state. That is no two electrons may have quantum numbers with the same value. This important statement may be used to predict the numbers of electrons in the shells of an atom. Let’s think about the X-shell and L-shell. (a) In the K-shell, n = 1. The only possible values for l and m are 0, s can be +L or -L, and so only two electrons can exist in this shell. (b) In the L-shell, n = 2. In this shell eight electrons are possible, as shown by the following table: n L m s n L 2 2 m s 0 0 +½ 2 1 -1 +½ 2 0 0 -½ 1 -1 -½ 2 1 0 +½ 2 1 0 -½ 2 1 +1 +½ 2 1 +1 -½ One result of this principle is that you can never squeeze two particles together to such an extent that they occupy the same state - objects must have a finite volume! It also means that if the exclusion priciple did not apply then all electrons in an atom would end up in the lowest possible energy state. Chemistry would be changed forever and the world as we know it would not exist.