Chapter 11, Problem 31A

Interpretation Introduction

Interpretation: Association of $n$ with the energy of a principal level 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 31A

As $n$ increases, energy of principal energy level around nucleus too in increases because of increases in distance of energy state from nucleus. Therefore, higher $n$ means higher energy of shell and lower $n$ means lower energy of shell.

Explanation of Solution

In an atom principal quantum number indicates principal energy level in which electron in present. It tells about size of orbital, approximate energy of electron in orbital and the number of electron an orbital can contain.

  $n=1$ means electron is present in lowest energy shell as it is closest to the nucleus and hence attracted by highest amount nuclear charge.

  $n=2$ means electron is present in second energy shell and little farther in distance from shell 1 and hence attracted by slightly lower amount of nuclear charge than for electron in $n=1$ . Similarly, it can be inferred for $n=3,\mathrm{4...}$ and so on.

So as $n$ increases the energy of the principal energy level around nucleus too in increases because of increases in distance of energy state from nucleus.

Therefore, higher $n$ means higher energy of shell and lower $n$ means lower energy of shell.

Conclusion

As $n$ increases, energy of principal energy level around nucleus too in increases because of increases in distance of energy state from nucleus. Therefore, higher $n$ means higher energy of shell and lower $n$ means lower energy of shell.