The relationship between atomic weight, equivalent weight, and valency is defined by the formula: Atomic Weight = Equivalent Weight × Valency. This relationship is fundamental in classical stoichiometry for determining the atomic masses of elements based on their combining capacities.

Magnesium (atomic number 12) is an alkaline earth metal in Group 2 with a valence configuration of ns2. Beryllium (atomic number 4) is also in Group 2. Elements in the same group share similar valence electron configurations and, consequently, exhibit similar chemical properties, such as forming +2 ions and reacting with oxygen to form oxides.

Johann Wolfgang Döbereiner observed that certain groups of three elements, known as 'triads,' displayed similar chemical properties. He noted that the atomic weight of the middle element was approximately the average of the atomic weights of the first and third elements. This discovery, known as Döbereiner's Law of Triads, was one of the earliest attempts to classify elements based on their atomic weights and chemical properties.

Neon, Helium, and Xenon are all noble gases belonging to Group 18 of the periodic table, characterized by their stable, filled valence electron configurations. Zinc is a transition metal belonging to Group 12, which has significantly different chemical properties and electronic structure compared to the noble gases.

Group 18 of the modern periodic table contains the noble gases, including helium, neon, argon, krypton, xenon, and radon. These elements possess a stable valence shell electron configuration, typically a complete octet (or duplet for helium), which renders them chemically inert under standard conditions. Their lack of reactivity is due to their high ionization energy and low electron affinity.

John Newlands observed that iron (Fe) shares similar chemical properties with cobalt (Co) and nickel (Ni). However, in his table, he placed iron in a different group from cobalt and nickel, which was a significant limitation of his Law of Octaves as it failed to group chemically similar elements together correctly.

In Mendeleev's periodic table, Cobalt (Co) was placed before Nickel (Ni). This arrangement was based on the atomic masses known at the time, although it technically violated the order of increasing atomic mass, which was later corrected by the modern periodic law.

When Mendeleev published his first periodic table in 1869, he arranged the 63 elements known at that time based on their atomic weights and chemical properties, leaving gaps for elements that had not yet been discovered.

Newlands' Law of Octaves states that every eighth element starting from a given element possesses similar properties. If we count the elements, the tenth element is the eighth element after the third element (3 + 7 = 10, but in the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, the eighth element after the third is the tenth). Therefore, the third and tenth elements share similar chemical characteristics.

The zigzag line, often called the staircase line, acts as a boundary in the periodic table. Elements to the left of this line are primarily metals, while elements to the right are non-metals. Elements touching the line are often classified as metalloids.