For the magnetism of alkali metal clusters, it is difficult to determine the number of atoms and the magnetic moment of isolated atoms cluster. In this paper, we investigate the magnetic moment of single atomic molecule ⁸⁷Rb ₁and 14 kinds of cluster particles ( ⁸⁷Rb) _n' ( n' = 2, 3, 4, ···, 15) in a saturated rubidium vapor sample at about 328 K, by using optical magnetic resonance spectroscopy. The experimental results show that there is a relationship f _n' = f*/ n' between the resonant frequencies f _n' of 14 kinds of cluster particles ( ⁸⁷Rb) _n' and the resonant frequencies f* of ⁸⁷Rb ₁. The magnetic moment and their resonance amplitudes show two different relationships with the n' odevity. When the particles have an odd number of 5s electrons, they must have spontaneous magnetic moment, and the value of magnetic moment increases with nand decreases inverse proportionally with the combined angular momentum Fof the cluster particles. The amplitude obtained from resonance spectrum complies with the variation law of magnetic moment value. On the other hand, for the cluster particles with nbeing even number, the magnetic moment value becomes 0 and the amplitude is also 0 in the most cases, except for the cluster particles ⁸⁷Rb ₂with n= 2 i.e. two 5s electrons, which is caused by the Jahn-Teller effect of the linear molecules, and the magnetic moment value is consistent with the calculation results of the odd number particles. When n> 2, the coupling effect between the magnetic moments of the Rb cluster shows a long-range ordered antiferromagnetic property with the increase of the number of 5s valence electrons n. The electron configuration and molecular state of the ground state and the lowest excited state of 14 kinds of 2—15 atoms cluster particles ⁸⁷Rb _n, as well as the stability of each molecular state and the possibility of visible Zeeman effect are obtained by using the molecular orbital-state theory analysis and constructing the ⁸⁷Rb _n–1+ ⁸⁷Rb _natomic cluster model. Furthermore, based on the magnetic moment of diatomic molecules ruler, it is found that when n= n' , the magnetic moment of ( ⁸⁷Rb) _n' and ⁸⁷Rb _nare in strict consistency (the average relative error is only 0.6765%), confirming the corresponding relationship between ( ⁸⁷Rb) _n' and ⁸⁷Rb _n. This research will be of great value in the magnetic research of cluster particles.