Quantum Numbers: Why (3,-2,0,1/2) is Invalid

[Feodalherren]

Homework Statement

Why isn't (3, -2 , 0 , 1/2) a valid quantum number?

Homework Equations

The Attempt at a Solution

n=3

so l = -2 is valid.

-l≤Ml≤l

2≤Ml≤-2
nonsensical statement. I don't know what to do...

 

[Saitama]

Homework Statement

Why isn't (3, -2 , 0 , 1/2) a valid quantum number?

Homework Equations

The Attempt at a Solution

n=3

so l = -2 is valid.

-l≤Ml≤l

2≤Ml≤-2
nonsensical statement. I don't know what to do...

No, l=-2 is not valid. l is always non-negative.

 

[Feodalherren]

Ah so it's that simple... Thanks.

 

[Christian0412]

I agree.
n = 3
l = 0, 1, 2
ml = -2, -1, 0, 1, 2
ms = -1/2 or 1/2

l cannot be negative, but ml can be.

 

[DeeNos]

The set of quantum numbers (n, l, ml, ms) is used to describe the energy levels, subshells, orbital orientations, and spin states of an electron in an atom. Each quantum number has a specific range of values that it can take on, and (3, -2, 0, 1/2) does not fall within these ranges.

The first quantum number, n, represents the principal energy level and can only take on positive integer values (1, 2, 3, etc.). Therefore, n=3 is a valid value.

The second quantum number, l, represents the angular momentum quantum number and is related to the shape of the orbital. It can only take on values from 0 to n-1. In this case, n=3, so l can only be 0, 1, or 2. -2 is not a valid value for l.

The third quantum number, ml, represents the magnetic quantum number and describes the orientation of the orbital in space. It can take on values from -l to l. In this case, l=-2, so ml can only be -2, -1, 0, 1, or 2. 0 is a valid value for ml.

The fourth quantum number, ms, represents the spin quantum number and describes the spin of the electron. It can only take on two values, +1/2 or -1/2. 1/2 is a valid value for ms.

Therefore, the quantum number set (3, -2, 0, 1/2) is invalid because -2 is not a valid value for l. The correct set of quantum numbers for an electron in the third energy level would be (3, 0, 0, 1/2).