The quantum number that tends to specify the orientation in space for an orbital is the

The state of an electron in an atom is defined by four quantum numbers. The principal quantum number (n) determines the main energy level and size of the orbital [t5][t6]. The azimuthal quantum number (l), also known as the orbital or angular momentum quantum number, defines the general geometric shape of the orbital [t1][t8]. The magnetic quantum number (m_l) specifically describes the orientation of the orbital in three-dimensional space [t1][t5]. It can take integer values ranging from -l to +l, which corresponds to the number of possible orientations the orbital angular momentum vector can have [t3][t4]. For instance, in a p-subshell where l=1, the magnetic quantum number allows for three distinct orientations [t3]. This orientation effect was historically first observed through the splitting of spectral lines in the presence of a magnetic field [t7].

Sources

1. [1] https://satheejee.iitk.ac.in/article/chemistry/chemistry-magnetic-quantum-number/