An electron has the quantum numbers 2:1:0:+1/2. In which suborbital is this electron found?

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valentin68 | College Teacher | (Level 3) Associate Educator

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First number from the 4 quantum number is the so called principal quantum number. It tells which principal energy level the electron is and is denoted by n. n=2 means the second energy level.

Second number of the set, is the angular quantum number (denoted by l). It can take values between 0...,n-1 and quantifies the angular momentum of the electron. It tells in which orbital the electron is located. l=1 means the orbital is p.

Third number quantifies the projection of the angular momentum on a certain axis (usually the z axis is taken). This number is denoted by ml. ml can take values from -l,..,0,...,+l (thus 2l+1 values). If ml=0 it means the projection of angular momentum on z axis is 0. It means the electron is either in the `p_x` or `p_y` suborbital.

Fourth number refers to the projection of the spin of the electron (which is always 1/2) on the same axis as above (z axis). This number is denoted with ms. ms can take only two values +1/2 and -1/2 telling if the spin is parallel with z axis or anti-parallel to it.
(ms=+1/2 means the spin is parallel with the z axis)

In conclusion for quantum numbers 2:1:0:+1/2 the electron is either in the `p_x` or `p_y` suborbital.