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Modern periodic law states:

“The physical and chemical properties of the elements are periodic functions of their atomic numbers”.

But I don't think this is so! (Forgive me for my stupidity. But please try to understand what I am saying and if you find any mistakes then please let me know).

If I consider the property of Li then I find that after 7 element there comes an element Na which have similar properties like Li. Now according to periodic law I must get another element which has similar properties to that of Li after 14 elements. And indeed I found one named K . Now again the same thing must happen (no?) ie, there must be an element which have similar properties to Li and is 21 elements away(Mn). But I don't find such element! Why?

The properties of Element is periodic so why then this "periodicity" doesn't hold in case of Li?

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    $\begingroup$ There is a pattern, but the period is not a constant. $\endgroup$ – orthocresol♦ Jan 21 at 12:47
  • $\begingroup$ @orthocresol but the word PERIODIC means : occurring or recurring at regular intervals [ merriam-webster.com/dictionary/periodic ]. Why then scientist are using such word which can led confusion in a law? $\endgroup$ – HiterDean Jan 21 at 12:51
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    $\begingroup$ Well, lexico.com/en/definition/periodic suggests "appearing or occurring at intervals" as their definition, so not as specific. Yes, English can be a bit weird, but the fact remains that technical definitions and uses may diverge from standard definitions and usages. Language is not static. $\endgroup$ – Jon Custer Jan 21 at 14:08
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    $\begingroup$ I think most people understand that when someone says they go to the doctor periodically, that does not imply exactly equally-spaced intervals. $\endgroup$ – Nicolau Saker Neto Jan 21 at 14:53
  • $\begingroup$ @JonCuster Science starts from words used in daily life and then make changes to it for it's own use. Indeed. But in this case a better word is "intermittent": .... stopping and starting repeatedly or with periods in between. [ google.com/amp/s/dictionary.cambridge.org/amp/english/… ] $\endgroup$ – HiterDean Jan 22 at 2:55
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First you need to understand what a periodic function is in mathematics. For example, if you are standing at any point P on a circle, you start walking on the circumference and count the degrees you completed. Once you complete 360 degrees, and you will find yourself on exactly the same point P. Sines, cosines and many other functions are periodic. This term existed before the chemists started using the term periodic law in the early 1800s or perhaps well before that. If $f(x)$ is a function with period $T$, then $f(x+T)= f(x)$ for a periodic function in a defined range of $[a,b]$. The period $T$ may change to $T'$, when x is in a different range say, $[c,d]$. This is an example of a discontinuous periodic function. As you will see, periodic properties of the elements form a discontinuous periodic pattern in a loose sense.

Now come to the periodic law: "The law that the chemical elements, when listed in order of their atomic numbers (originally, atomic weights), fall into recurring groups, so that elements with similar properties occur at regular intervals." [unabridged OED].

Instead of $x$ for a mathematical function, the independent variable is the atomic numbers Z (Zahl for a number in German) for the chemists. So this periodic law has a very loose connection with mathematical periodic function, because none of the values are actually repeated. Each element is unique, but in a loose way, their properties or even a better word is trends "repeat" themselves after a certain number of elements. See this chart for example. Atomic radii vs. Z, do you see a loose periodic pattern?

enter image description here

Once you have got the idea of periodic function in a loose way for the chemical elements, get ready to the see the physicists style of periodic table. It explains why some properties loosely repeat themselves.

Each element in the column, corresponds to filling of a certain orbital, for example look at the column $s^1$. All elements falling in that column correspond to the filling of $s^1$ electrons. Then move to the next column $s^2$, all elements listed there corresponding to filling of $s^2$. Can you see a pattern? In this sense, one calls it periodic function in a modern way, that certain elements repeatedly fall in $s^1$ column, some elements repeatedly fall in $s^2$ column.

enter image description here

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