Quantum numbers, number

Spin quantum number Number indicating the number of allowed orientations of a particular nucleus in a magnetic field. For example, H has an I value of lk, allowing for two possible orientations, whereas 14N has an I of 1, allowing three possible orientations. 

Quantum numbers Numbers that describe the energies of electrons in atoms they are derived from quantum mechanical treatment. 

Bohr s 1923 Electronic Configurations Based on Two Quantum Numbers. Numbers of electrons is consecutive energy levels, beginning closest to the nucleus. 

Quantum number Number, in most cases an integer, specifying the fact that the associated energy, momentum, or other property of a system is restricted to certain values. 

M total magnetic quantum numbers Mi, Mg, Mj) n principal quantum number, number of moles N molecular rotational angular momentum, number of atoms in molecule, Avogadro s number (Af ) p momentum, I = 1 atomic orbital, number of phases, steric factor... 

Rotational quantum numbers Numbers that specify various angular momenta and distinguish the rotational energy levels. 

An s orbital is spherically symmetrical and can contain a maximum of two electrons with opposed spins. A p orbital has a solid figure-of-eight shape there are three equivalent p orbitals for each principal quantum number they correspond to the three axes of rectangular coordinates. 

The d and f orbitals have more complex shapes there are five equivalent d orbitals and seven equivalent f orbitals for each principal quantum number, each orbital containing a maximum of 2 electrons with opposed spins. 

The above definitions must be qualified by stating that for principal quantum number I there are only s orbitals for principal quantum number 2 there are only s and p orbitals for principal quantum number 3 there are only s, p and d orbitals for higher principal quantum numbers there are s, p, d and f orbitals. 

Pauli exclusion principle In any atom no two electrons can have all four quantum numbers the same. See exclusion principle. 

Nuclear magnetic resctnance involves the transitions between energy levels of the fourth quantum number, the spin quantum number, and only certain nuclei whose spin is not zero can be studied by this technique. Atoms having both an even number of protons and neutrons have a zero spin for example, carbon 12, oxygen 16 and silicon 28. 

The rotational energy of a rigid molecule is given by 7(7 + l)h /S-n- IkT, where 7 is the quantum number and 7 is the moment of inertia, but if the energy level spacing is small compared to kT, integration can replace summation in the evaluation of Q t, which becomes... 

Figure Al.1.1. Wavefimctions for the four lowest states of the hamronie oseillator, ordered from the n = Q ground state (at the bottom) to tire u = 3 state (at the top). The vertieal displaeement of the plots is ehosen so that the loeation of the elassieal turning points are those that eoineide with the superimposed potential fimetion (dotted line). Note that the number of nodes in eaeh state eorresponds to the assoeiated quantum number.

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