Which set of numbers gives the correct possible values of \(l\) for \(n=3\)?
A. \(0,1,2\)
B. \(0,1,2,3\)
C. \(-2,-1,0,1,2\)
D. \(-3,-2,-1,0,1,2,3\)
Answer (1)
The problem relates to quantum mechanics, where 'l' represents the orbital angular momentum quantum number and 'n' is the principal quantum number.
For a given 'n', 'l' can take integer values from 0 to n-1.
Given n=3, the possible values for l are 0, 1, and 2.
The correct set of numbers representing these values is 0 , 1 , 2 .
Explanation
Understanding the Problem The question asks for the correct set of possible values of a variable (which is not explicitly defined but implied as 'l') for n = 3 . We need to understand what 'l' represents in relation to 'n'. In the context of angular momentum in quantum mechanics, 'l' represents the orbital angular momentum quantum number, and 'n' represents the principal quantum number.
Relating l and n In quantum mechanics, for a given principal quantum number n , the orbital angular momentum quantum number l can take integer values from 0 to n − 1 .
Determining Possible Values for l Given n = 3 , the possible values for l are 0 , 1 , 2 .
Selecting the Correct Set Now, we compare the possible values we found with the given options:
0 , 1 , 2 - This matches our result.
0 , 1 , 2 , 3 - This includes 3, which is not a possible value since l can only go up to n − 1 = 3 − 1 = 2 .
− 2 , − 1 , 0 , 1 , 2 - This includes negative values, which are not possible for l .
− 3 , − 2 , − 1 , 0 , 1 , 2 , 3 - This includes negative values and 3, which are not possible for l .
Final Answer Therefore, the correct set of numbers that gives the possible values of l for n = 3 is 0 , 1 , 2 .
Examples
Understanding the possible values of quantum numbers like 'n' and 'l' is crucial in fields like chemistry and physics. For example, when studying the electronic configuration of atoms, 'n' determines the energy level of an electron, and 'l' determines the shape of the electron's orbital (s, p, d, etc.). Knowing these quantum numbers allows scientists to predict and explain the chemical behavior of elements and the formation of chemical bonds. In medical imaging, understanding electron behavior helps in developing better MRI and PET scan technologies.
