Which set of numbers gives the correct possible values of [tex]$l$[/tex] for [tex]$n=2$[/tex]?
A. 0
B. 0,1
C. [tex]$0,1,2$[/tex]
D. [tex]$0,1,2,3$[/tex]

The problem requires finding possible values of the quantum number l for n = 2 .
The range of l is from 0 to n − 1 .
Substituting n = 2 , the range becomes 0 ≤ l ≤ 1 .
The possible values for l are 0 and 1, so the answer is 0 , 1 ​ .

Explanation

Understanding the Problem The question asks for the possible values of the quantum number l for a given principal quantum number n = 2 . In quantum mechanics, the azimuthal quantum number l determines the shape of an atomic orbital and has values ranging from 0 to n − 1 , where n is the principal quantum number.

Determining the Range of Possible Values We are given that n = 2 . The possible values of l are integers that satisfy the condition 0 ≤ l ≤ n − 1 . Substituting n = 2 into this inequality, we get 0 ≤ l ≤ 2 − 1 , which simplifies to 0 ≤ l ≤ 1 .

Listing the Possible Values The integers that satisfy 0 ≤ l ≤ 1 are 0 and 1. Therefore, the possible values of l when n = 2 are 0 and 1.

Final Answer The correct set of numbers that gives the possible values of l for n = 2 is 0, 1.


Examples
In the realm of atomic structure, understanding quantum numbers is crucial for predicting the behavior of electrons within atoms. For instance, when designing materials with specific optical or electronic properties, scientists manipulate the quantum states of electrons. Knowing that for n = 2 , l can only be 0 or 1 helps in selecting appropriate elements and designing their electronic configurations to achieve desired material characteristics. This principle is applied in creating semiconductors, lasers, and other advanced technologies.

Answered by GinnyAnswer | 2025-07-07