This phenomenon that the number of elements contained in each cycle is different is caused by the different number of electron sublayers (energy levels) contained in different energy level groups. For example, the first cycle only has 1 1s sublayer; In the fourth stage, there are three sublayers: 4s, 4p and 3d.
The number of periods is represented by n, and the number of sub-layers is represented by l. The relationship between the number of cycles and the number of sublayers can be expressed as:
Several mathematical formulas of periodic table X ... (1)
Example 1, calculate the number of sublayers contained in the fourth energy level group (the fourth phase).
When N=4, the formula (1) is several mathematical formulas about the periodic table of elements.
It is consistent with the fact that the fourth cycle of electron filling is carried out in 4s, 4p and 3d, which is on such three sublayers.
Equation (1) is also applicable to other loops (readers can verify it themselves). Equation (1) truly and perfectly reflects the relationship between the number of periods and the number of sublayers in the periodic table of elements.
Second, calculate the number of elements contained in each cycle.
Since the maximum number of electrons that can be accommodated in each sub-layer is fixed, the formula for calculating the number of kinds of elements contained in different periods can also be derived from the above formula.
Let the number of elements contained in the nth cycle be ZN. There are:
Several Mathematical Formulas in the Periodic Table of Elements ... (2)
Example 2: Calculate the number of element types included in the fourth period.
Substituting N=4 into formula (2) is as follows
Several Mathematical Formulas of the Periodic Table of Elements
It is consistent with the fourth phase with 18 elements.
The calculation in other periods is also consistent with the actual situation.
Three. Calculation of atomic number of rare gas elements at the end of each cycle
There is a rare gas element at the end of each cycle. The atomic number of an element can also be calculated
Let the atomic number of the rare gas at the end of the nth cycle be XN. There are:
Several mathematical formulas about the periodic table of elements ... (3) r >; Because this formula has two series terms, it looks longer. But it only involves simple four-element calculation, which is actually not very troublesome to use. For example:
Example 3: Find the atomic number of rare gas element xenon in the fifth cycle.
Substituting N=5 into formula (3) is as follows
Several Mathematical Formulas of the Periodic Table of Elements
In fact, the atomic number of xenon at the end of the fifth cycle is 54.
The atomic number of rare gases in other periods can also be calculated by Formula (3).
Fourth, the calculation of atomic number of elements
Because the atomic number of an element has a simple relationship with the atomic number of rare gas elements in the same period. Therefore, the formula for calculating the atomic number of an element can be derived from the above formula (3).
Let the atomic number of an element be m, the number of cycles in which it is located be n (the atomic number of the rare gas related to it is XN or XN- 1), and its main group number be h, then
There are several mathematical formulas about the periodic table of elements in p or ds region …