What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4

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Identify the principal quantum number (n) for each part of the question. The principal quantum number, n, determines the size and energy level of the orbital.

Recall that the azimuthal quantum number (l) can take on any integer value from 0 to n-1. This quantum number determines the shape of the orbital.

For n=1, calculate the possible values of l by substituting n into the formula l = 0 to n-1. Since n-1 equals 0, l can only be 0.

For n=2, calculate the possible values of l. Substitute n into the formula l = 0 to n-1. Since n-1 equals 1, l can be 0 or 1.

For n=3 and n=4, repeat the same process as above. For n=3, l can be 0, 1, or 2. For n=4, l can be 0, 1, 2, or 3.

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주요 개념

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Principal Quantum Number (n)

The principal quantum number, denoted as 'n', indicates the energy level of an electron in an atom and can take positive integer values (1, 2, 3, ...). It determines the size and energy of the orbital, with higher values corresponding to higher energy levels and larger orbitals.

Azimuthal Quantum Number (l)

The azimuthal quantum number, represented as 'l', defines the shape of the electron's orbital and can take integer values from 0 to (n-1) for each principal quantum number 'n'. For example, if n=2, l can be 0 or 1, corresponding to s and p orbitals, respectively.

Orbital Types

Different values of the azimuthal quantum number 'l' correspond to different types of orbitals: 'l=0' (s), 'l=1' (p), 'l=2' (d), and 'l=3' (f). Understanding these orbital types is essential for predicting the electron configuration and chemical properties of elements.