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Chapter 10: Problem 40

The number of sublevels in a principal energy level (increases/decreases) as \(n\) increases.

Short Answer

Expert verified
The number of sublevels in a principal energy level increases as \(n\) increases. This is because the number of possible sublevels is determined by the Azimuthal Quantum Number (l), which ranges from 0 to (\(n\)-1). As the principal quantum number (\(n\)) increases, the range of values for \(l\) also increases, resulting in more sublevels.

Step by step solution

01

Understanding Principal Quantum Number

Principal quantum number (n) is a positive integer that determines the energy level of an electron in an atom. It indicates the shell or the energy level in which the electron can be found. As the value of n increases, the electron is found in a higher energy level, further from the nucleus of the atom.
02

Understanding Sublevels and Azimuthal Quantum Number

Sublevels are regions within an energy level where electrons with particular orbital shapes reside. The number of possible sublevels in a principal energy level is determined by the Azimuthal Quantum Number (l). The value of l ranges from 0 to (n-1). Each value of l represents a sublevel, with l=0 representing the s sublevel, l=1 representing the p sublevel, l=2 representing the d sublevel, and l=3 representing the f sublevel.
03

Determining the Number of Sublevels

To determine the number of sublevels in a principal energy level, simply count the values of l for that particular value of n. For example, when n=1, l can have values 0 (only the s sublevel). When n=2, l can have values 0 and 1 (the s and p sublevels). When n=3, l can have values 0, 1, and 2 (the s, p, and d sublevels), and so on.
04

Relationship between Principal Quantum Number and Sublevels

From the discussion above, it is clear that as the value of n increases, the number of possible values for l (sublevels) also increases. Thus, the number of sublevels in a principal energy level increases as n increases.

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