Question

The total number of orbitals in the fifth energy level is:
a.) 5
b.) 10
c.) 18
d.) 25

Answer 1

Hint: In order to solve the given problem and find out the number of orbitals in the fifth energy level first we will understand the basic structure of the orbitals and the energy levels. First on the basis of the energy level we will relate the energy level with the principal quantum number number. For the fifth quantum number we will find the corresponding azimuthal quantum numbers. Now for each of the azimuthal quantum numbers we will relate the various orbitals and also the number of each orbitals. Finally we will add them to find out the total number of orbitals.


Complete step by step answer:
Only such discrete energy quantities, called energy levels, may be embraced by a quantum mechanical device or particle that is bound, that is, spatially confined.
Energy levels (also known as shells of electrons) are set distances from an atom's nucleus where electrons can be contained. In an atom, electrons are small, negatively charged particles that pass at the centre of the positive nucleus. Energy levels are a little like the staircase steps.
The energy level number corresponds with the principal quantum number represented by “n”.
So in the given case n = 5.
We know that in the quantum model of an atom the azimuthal number relating to the principal quantum number is represented by “l”.
And the range of this term is:
$l = 0$ to $l = \left( {n - 1} \right)$ .
So, for the above case we have:
$l = 0,1,2,3,4$
And these azimuthal number are related to some term as follows:
$
  l = 0 \Rightarrow 5s \\
  l = 1 \Rightarrow 5p \\
  l = 2 \Rightarrow 5d \\
  l = 3 \Rightarrow 5f \\
  l = 4 \Rightarrow 5g \\
 $
For each of the orbital states we have a different number of total orbitals which is increasing as the azimuthal number increases.
The number of orbitals are as follows:
\[
  s \Rightarrow 1{\text{ orbitals}} \\
  p \Rightarrow 3{\text{ orbitals}} \\
  d \Rightarrow 5{\text{ orbitals}} \\
  f \Rightarrow 7{\text{ orbitals}} \\
  g \Rightarrow 9{\text{ orbitals}} \\
 \]
So, the total number of orbitals in the fifth energy level will be sum of all the orbitals for different azimuthal state; which is equal to:
\[
   = \left( {{\text{1 + 3 + 5 + 7 + 9}}} \right){\text{ orbitals}} \\
   = {\text{25 orbitals}} \\
 \]
Hence, the total number of orbitals in the fifth energy level is 25.
So, the correct answer is “Option D”.

Note: In order to solve such types of problems students must be aware of the quantum model of the atom and also about the basic structure of the atoms. This structure is totally based upon the schrodinger wave equation and probability theorem. The students must remember the relation between the quantum number and the orbitals. Complex types of orbitals (sometimes called electron clouds), volumes of space in which an electron is likely to be present, are used in the quantum mechanical model of the atom. So, rather than certainty, this model is based on likelihood.