In the ground state, an element has 13 electrons in its M-shell.The element is :
A) manganese
B) cobalt
C) nickel
D) iron

Hint: M-shell is the third energy level. It can have a maximum of 18 electrons. Also recall that lower energy levels are filled first.

Complete step by step answer:
In an atom, the electrons surround the nucleus in different orbitals or energy levels. These orbitals are known as either first, second, third ... energy levels or K,L,M, N... shells. K-shell is the first energy level and can have a maximum of 2 electrons. L-shell is the second energy level and can have a maximum of 8 electrons. M-shell is the third energy level and can have a maximum of 18 electrons.

In the ground state, an element has 13 electrons in its M-shell. It has 2 electrons in the K shell and 8 electrons in the L shell. Since it has 13 electrons in its M-shell, it is a d block element with 18-13=5 electrons in 3d subshell. The elements belonging to 3d subshell also have two electrons in the N shell, in 4s orbital. Hence, the total number of electrons in the element is 2+8+13+2=25.
The atomic number of the element is 25. Atomic number is equal to the number of electrons present in a neutral atom. The atomic numbers of manganese, iron, cobalt and nickel are 25, 26, 27, and 28 respectively.
Hence, the element with 13 electrons in its M-shell has an atomic number of 25 and is manganese.

Thus, option A is the correct answer.

Note:
Do not put more than 2 electrons in K-shell and more than 8 electrons each in L -shell since this is the maximum number of electrons that can be accommodated.