Chapter 11, Problem 32A

Interpretation Introduction

Interpretation: The number of sublevels in principal energy level increases or decreases as $n$ increases is to be explained.

Concept introduction: 3-D space around nucleus in which probability of finding an electron of particular energy is maximum, is called orbital. Quantum numbers are group of 4 numbers which tell everything about electron present in an atom. Principal quantum numbers indicates principal energy level in which electron in present. It is denoted by $n$ .

Answer to Problem 32A

The number of sublevels in principal energy level increases as $n$ increases. This is because farther the principal energy level from nucleus, higher is its energy due to decrease in nuclear hold on it and hence the size increases. So with increased size, more sub-shells that are discrete space for electrons to occupy too increase.

Explanation of Solution

The number of sublevels in principal energy level increases as $n$ increases. Farther the principal energy level from nucleus, higher is its energy, as nuclear hold on it decreases and size increases. So with increased size, more sub-shells that are discrete space for electrons to occupy too increase.

This can be understood by the fact that level with $n=1$ value has 1 sub shell that is $1s$ , level with $n=2$ value has 2 sub-shells that is $2s2p$ , level with $n=3$ value has 3 sub-shell that is $3s3p3d$ and so on.

Conclusion

The number of sublevels in principal energy level increases as $n$ increases. This is because farther the principal energy level from nucleus, higher is its energy due to decrease in nuclear hold on it and hence the size increases. So with increased size, more sub-shells that are discrete space for electrons to occupy too increase.