Chapter 11, Problem 30A

Interpretation Introduction

Interpretation: Possible sublevels for each value of $n$ are to be estimated.

Concept introduction: There is total of 4 quantum numbers: principal quantum number $\left(n\right)$ , angular momentum quantum number $\left(l\right)$ , magnetic quantum number $\left(m\right)$ and electron spin quantum number $\left(m_s\right)$ .

  $n$ indicates energy and distance from nucleus. It represents the shell with allowed values equal to positive whole numbers.

  $l$ indicates shape of orbital. Its allowed values are all positive integer from 0 to $n-1$ .The table for the $l$ values is as follows:

  $\begin{array}{cccccccc}l& 0& 1& 2& 3& 4& 5& 6\\ \text{Subshell}& s& p& d& f& g& h& i\end{array}$

  $m$ indicates the arrangment of orbitals. The values for $m$ for any orbital is given by any integer value from $-l$ to $l$ .

  $m_s$ has only 2 possible values, $+\frac{1}{2}$ and $-\frac{1}{2}$ . It describes the spin of each electron in the orbital.

Answer to Problem 30A

The possible / allowed value of shells is as follows:

  $\begin{array}{cc}\text{value}\text{of}n& \text{possible}\text{sublevel}\\ 1& 1\left(1s\right)\\ 2& 2\left(2s,2p\right)\\ 3& 3\left(3s,3p,3d\right)\\ 4& 4\left(4s,4p,4d,4f\right)\end{array}$

Explanation of Solution

Atom of an element contains shells or energy levels ( $n$ ) which contain sublevels or orbital’s to accommodate electrons.

The possible / allowed value of shells is as follows:

  $\begin{array}{cc}\text{value}\text{of}n& \text{possible}\text{sublevel}\\ 1& 1\left(1s\right)\\ 2& 2\left(2s,2p\right)\\ 3& 3\left(3s,3p,3d\right)\\ 4& 4\left(4s,4p,4d,4f\right)\end{array}$

Conclusion

The possible / allowed value of shells is as follows:

  $\begin{array}{cc}\text{value}\text{of}n& \text{possible}\text{sublevel}\\ 1& 1\left(1s\right)\\ 2& 2\left(2s,2p\right)\\ 3& 3\left(3s,3p,3d\right)\\ 4& 4\left(4s,4p,4d,4f\right)\end{array}$