In this work, the properties of isomeric states of spherical nuclei associated with the 1g9/2 orbital are studied. A systematics of the lifetimes of isomeric states in A-odd nuclei with the number of protons Z=33-49 is given. A comparison of the experimental values of the half-lives based on a single-particle model of the isomeric transition probability is given. A similar systematics is given for A-odd nuclei with the number of neutrons N=35-49. The nature of isomerism in neighboring odd-odd nuclei is associated with single-particle excitation and vector addition of the angular momenta of odd protons and neutrons, one of which does not change its state. Our results indicate that the isomeric states in spherical nuclei have a single-particle structure. The high multipolarity (M4, E3) of isomeric transitions explains their low probability, and large changes in lifetimes are associated with different excitation energies of the isomers.