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Understanding the physical mechanism behind atomic-size dependence of the bandgap, phonon frequency, and mechanical strength in various monolayered MA2Z4 is of crucial importance for their electronic and photoelectronic applications. The density functional theory calculation results confirm that these physical quantities gradually decrease with the increasing periodicity of the atomic size (or radius) of the A or Z of MA2Z4. In order to clarify the common origin of the atomic-size dependence of these quantities, we establish these quantities as functions of bond length and bond energy by developing a bond relaxation theory approach. Theoretical reproduction of periodic trends confirms that bond expansion and energy weakening dominate their atomic-size dependence. The proposed approach is not only helpful to understand the physical origins of atomic-size dependence in different MA2Z4 monolayers but also can be extended to study the periodic trends of the related physical properties in other systems. [ABSTRACT FROM AUTHOR]