1. The angular momentum quantum number is called "azimuthal" because it describes the electron's motion around the nucleus in terms of its angular momentum. The word "azimuth" refers to the angle between a point and a reference direction in a plane, and in the case of the electron, the reference direction is the line connecting the nucleus to the electron. The angular momentum quantum number, denoted by the letter "l", describes the electron's angular momentum in terms of its "azimuthal quantum number", which is a measure of the electron's angular momentum in the plane perpendicular to the internuclear axis.

2. The angular momentum quantum number cannot take the value of 0 because this would imply that the electron has no angular momentum, which is not possible for an electron moving around the nucleus. Electrons must have some angular momentum due to their motion around the nucleus, and the angular momentum quantum number describes the specific amount of angular momentum that the electron has.

3. An electron cannot have an angular momentum quantum number of 0 because this would imply that the electron is in a state of zero angular momentum, which is not possible for an electron moving around the nucleus. The electron must have some non-zero angular momentum, and the angular momentum quantum number describes the specific amount of angular momentum that the electron has.