Question

What is the atomic number of another element present in the same group as the element with \[{\text{Z = 13}}\]?
A. ${\text{Z = 50}}$
B. ${\text{Z = 32}}$
C. ${\text{Z = 49}}$
D. ${\text{Z = 20}}$

Answer 1

Hint: Classification of elements is the arranging of elements into different groups on the basis of the similarities in their properties. There are seven periods and eighteen groups. Modern periodic law was the proposed arrangement of elements based on the atomic number.

Complete step by step solution:
The development of periodic table was based on several theories as given below:
1.Triads
2.Law of octaves
3.Lothar Mayer’s atomic volume curve
4.Mendeleev’s periodic table
5.Mosley’s modern periodic table

Modern periodic law explains that the physical and chemical properties of the elements are based on their atomic numbers. If the outer electronic configuration of atoms are similar, then the properties will also be the same. The electrons are distributed over different orbits. Atomic number denotes the number of protons. We know that the number of protons equals the number of electrons.
It is given that the atomic number of an element is \[{\text{Z = 13}}\], i.e. the electrons filled can be expressed as $2,8,3$. This indicates that the valency of the element is $3$. Thus it lies in the group $3$. So another element in the same group has the same valency, $3$. Since it has three shells, it also lies in period three.
In group $3$, ${{\text{1}}^{{\text{st}}}}$ element has atomic number $2 + 3 = 5$, ${2^{{\text{nd}}}}$ element $ - 5 + 8 = 13$, ${3^{{\text{rd}}}}$ element -$13 + 18 = 31$, fourth element -$31 + 18 = 49$, fifth element -$49 + 36 = 81$.
Thus we can conclude that the atomic number of elements of the same group having atomic number, \[{\text{Z = 13}}\] will be ${\text{Z = 49}}$.

So the correct option is C.

Note: The maximum number of electrons that can be occupied in a shell is denoted by ${\text{2}}{{\text{n}}^2}$, where ${\text{n}}$ is an integer. First period has two elements, the second and third has eight elements, and so on. So we can calculate the atomic number of elements in the same group by adding these numbers. The sequence is $2,8,8,18,18,32,32$ with respect to the period number.