Question

a) How many subshells are associated with n = 4?
b) How many electrons will be present in the sub-shells having ${m_s}$ value of $ - \dfrac{1}{2}$ for n = 4?

Answer 1

Hint- If n is the given number then number of sub shells can be found by counting all the digits from 0 to $l = n - 1$ , and Number of orbitals in the nth shell can be calculated as ${n^2}$ . we will use these concept and formula to find the answer.

Complete answer:
a) $n = 4$
As we know that If n is the given number then the number of subshells can be found by counting all the digits from 0 to $l = n - 1$ .
When $n = 4$
$l = 0,1,2,3$
$
  l = 0;4s - {\text{subshell}} \\
  l = 1;4p - {\text{subshell}} \\
  l = 2;4d - {\text{subshell}} \\
  l = 3;4f - {\text{subshell}} \\
 $
Hence, for $n = 4$, there are 4-subshells.

b) Number of orbitals in the nth shell $ = {n^2}$
For $n = 4$
Number of orbitals $ = {n^2} = {4^2} = 16$
Each orbital has one electron with \[{m_s} = - \dfrac{1}{2}\]

Hence, there will be 16 electrons present in the subshell with \[{m_s} = - \dfrac{1}{2}\]

Note- The given structure of atom was on the basis of the quantum model of atom. The Austrian physicist Erwin Schrödinger theorized that the behavior of electrons within atoms could be explained by mathematically treating them as waves of matter. This model is known as the quantum mechanical or wave mechanical model, which is the basis for the modern understanding of the atom. According to this model shells are a collection of subshells with the same quantity principle and subshells are a collection of orbitals with the same quantity principle and the same quantity of angular momentum.