by 'f', and 4 by 'g'. For instance, one may speak of the subshell with and as a '2s subshell'. Each electron also has a spin quantum number, s, which describes the spin of each electron (spin up or spin down). The number s can be + or −. The Pauli exclusion principle states that no two electrons in an atom can have the same values of all four quantum numbers. If there are two electrons in an orbital with given values for three quantum numbers, (, , ), these two electrons must differ in their spin. The above conventions imply a preferred axis (for example, the z direction in Cartesian coordinates), and they also imply a preferred direction along this preferred axis. Otherwise there would be no sense in distinguishing from . As such, the model is most useful when applied to physical systems that share these symmetries. The Stern–Gerlach experimentwhere an atom is exposed to a magnetic fieldprovides one such example. Real orbitals In addition to the complex orbitals described above, it is common, especially in the chemistry literature, to use real atomic orbitals. These real orbitals arise from simple linear combinations of complex orbitals. Using the Condon–Shortley phase convention, real orbitals are related to complex orbitals in the same way that the real spherical harmonics are related to complex spherical harmonics. Letting denote a complex orbital with quantum numbers , , and , the real orbitals may be defined by If , with the radial part of the orbital, this definition is equivalent to where is the real spherical harmonic related to either the real or imaginary part of the complex spherical harmonic . Real spherical harmonics are physically relevant when an atom is embedded in a crystalline solid, in which case there are multiple preferred symmetry axes but no single preferred direction. Real atomic orbitals are also more frequently encountered in introductory chemistry textbooks and shown in common orbital visualizations. In real hydrogen-like orbitals, quantum numbers and have the same interpretation and significance as their complex counterparts, but is no longer a good quantum number (but its absolute value is). Some real orbitals are given specific names beyond the simple designation. Orbitals with quantum number equal to are called orbitals. With this one can already assign names to complex orbitals such as ; the first symbol is the quantum number, the second number is the symbol