Principle quantum number The

After the separation of the kinetic energy operator due to the center-of-mass motion from the Hamiltonian, the Hamiltonian describes the internal motions of electrons and nuclei in the system. These in the BO approximation can be separated into the vibrational and rotational motions of the nuclear frame of the molecule and the electronic motion that only parametrically depends on the instantenous positions of the nuclei. When the BO approximation is removed, the electronic and nuclear motions become coupled and the only good quantum numbers, which can be used to quantize the stationary states of the system, are the principle quantum number, the quantum number quantizing the square of the total (nuclear and electronic) squared angular momentum, and the quantum number quantizing the projection of the total angular momentum vector on a selected direction (usually the z axis). The separation of different rotational states is an important feamre that can considerably simplify the calculations. 

The first shell or energy level out from the nucleus is called the K shell or energy level and contains a maximum of two electrons in the s orbital— that is, K = s2, where the K represents the shell number (or principle quantum number), the s describes the orbital shape of the angular momentum quantum number, and the 2 is the maximum number of electrons that the s orbital can contain. This particular sequence is K = s2, which means K shell contains 2 electrons in the s orbital. This is the sequence for the element helium. Look up helium in the text for more information. 

As discussed in Section 2.2.2.3.4, such transitions result in Auger electron emission or X-ray emission (fluorescence). In the Auger process, in which the X-ray notation is prevalent, the resulting emission would be referred to as a KL L electron if the emitted electron came from the 2pj/2 level. For fluorescence, the emission is referred to as a KL X-ray, or if the Siegbahn X-ray convention were to be used (common in the X-ray community), this would be referred to as a Ka X-ray. In this notation, the Greek letter denotes allowed transitions from stationary states of the next principle quantum number (the order being a, p, Q, whereas the subscript refers to the relative intensity (1 being the most intense). 

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