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Chapter 8: Problem 27

What are the possible values of \(m\) for an electron in the \(n=4\) state?

Short Answer

Expert verified
The possible values of \(m\) for an electron in the \(n=4\) state are -3, -2, -1, 0, +1, +2, and +3.

Step by step solution

01

Identify the Principal Quantum Number (n)

In the given exercise, we have the principal quantum number (n) as 4. The principal quantum number determines the energy level and size of an electron's orbit.
02

Recall the Relationship between n, l, and m

For any given value of n, the Azimuthal Quantum Number (l) can take any integer value from 0 to (n-1). Additionally, the Magnetic Quantum Number (m) can take any integer value from -l to +l, including 0. In summary: - For n = 4, l can have values from 0 to 3. - For each l value, m can have values from -l to +l.
03

Find Possible m Values Based on l Values

We'll list out each possible l value (0 to 3) and their respective m values: 1. For l = 0 m can vary between -0 and +0, which gives the single value m = 0. 2. For l = 1 m can vary between -1 and +1, which gives the values m = -1, 0, +1. 3. For l = 2 m can vary between -2 and +2, which gives the values m = -2, -1, 0, +1, +2. 4. For l = 3 m can vary between -3 and +3, which gives the values m = -3, -2, -1, 0, +1, +2, +3.
04

Combine All Possible m Values

By combining all the possible m values listed above, we have: m = -3, -2, -1, 0, +1, +2, +3 These are the possible values of m for an electron in the n=4 state.

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