Question

total number of orbitals associated with the third shell will be _________.
(a) 2
(b) 4
(c) 9
(d) 3

Answer 1

In atomic theory and quantum mechanics, an atomic orbital is a mathematical function describing the location and wave-like behaviour of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus.

Complete step by step answer:
We have been asked about the number of orbitals associated with third shell,
So, for that,
We know that there can be two electrons in one orbital maximum. The s sublevel has just one orbital, so can contain 2 electrons max. The p sublevel has 3 orbitals, so can contain 6 electrons max. The d sublevel has 5 orbitals, so can contain 10 electrons max.
Now, the orbit around the nucleus within which the electron rotates is called shells or Energy levels." Each discrete distance orbit from the nucleus corresponds to a certain energy level. The electron which rotates in the lowest orbit has lowest energy level and in the outermost orbit, electrons have higher energy levels.
We know that, the total number of orbitals in nth shell: ${{n}^ {2}}$,
Where, n= shell/ principal quantum number,
So, we need to calculate the total number of orbitals in third shell,
So, n will be equal to 3,
Therefore, the orbitals would be: ${{3} ^ {2}} =9$.
So, the orbitals are one 3-s orbital, three 3-p orbital and five 3-d orbitals.
So, the correct answer is “Option C”.

Note: The outer energy levels have higher energy than the inner energy levels or shells. The electrons want to be closer to the nucleus because opposite charges attract each other. Farther the satellite less is the velocity and same is the case with the electron.