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 ⁸⁷Rb₁ and 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 ⁸⁷Rb₁. 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 n and decreases inverse proportionally with the combined angular momentum F of 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 n being even number, the magnetic moment value becomes 0 and the amplitude is also 0 in the most cases, except for the cluster particles ⁸⁷Rb₂ with 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_n atomic 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_n are 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.