The following quantum numbers are possible for how many orbital(s) $n = 3$ ,$l = 2$ and $m = +2$ are possible ?

Question

An element 'M' has 25% of the electrons filled in the third shell as in the second shell. The element 'M' is :

Answer 1

To determine how many orbitals are possible for the given set of quantum numbers $ n = 3 $, $ l = 2 $, and $ m = +2 $, we need to understand what each quantum number represents and how they relate to the orbitals:

Principal Quantum Number ($ n $): This number indicates the energy level or shell of the electron. Here, $ n = 3 $ refers to the third energy level.
Azimuthal Quantum Number ($ l $): This number defines the subshell or the shape of the orbital. It ranges from $ 0 $ to $ n-1 $. For $ n = 3 $, possible values of $ l $ are $ 0 $, $ 1 $, and $ 2 $. Here, $ l = 2 $ corresponds to the d-subshell.
Magnetic Quantum Number ($ m $): This number defines the orientation of the orbital in space and takes values from $-l$ to $+l$, inclusive. For $ l = 2 $, $ m $ can be $-2, -1, 0, +1, +2$.

Since $ m = +2 $, we are interested in the specific orientation of the d-orbital. Each unique combination of $ n $, $ l $, and $ m $ corresponds to one unique orbital.

Thus, there is only one orbital corresponding to the quantum numbers $ n = 3 $, $ l = 2 $, and $ m = +2 $.

Therefore, the correct answer is 1.

Answer 2

To determine how many orbitals are possible for the given set of quantum numbers $ n = 3 $, $ l = 2 $, and $ m = +2 $, we need to understand what each quantum number represents and how they relate to the orbitals:

Principal Quantum Number ($ n $): This number indicates the energy level or shell of the electron. Here, $ n = 3 $ refers to the third energy level.
Azimuthal Quantum Number ($ l $): This number defines the subshell or the shape of the orbital. It ranges from $ 0 $ to $ n-1 $. For $ n = 3 $, possible values of $ l $ are $ 0 $, $ 1 $, and $ 2 $. Here, $ l = 2 $ corresponds to the d-subshell.
Magnetic Quantum Number ($ m $): This number defines the orientation of the orbital in space and takes values from $-l$ to $+l$, inclusive. For $ l = 2 $, $ m $ can be $-2, -1, 0, +1, +2$.

Since $ m = +2 $, we are interested in the specific orientation of the d-orbital. Each unique combination of $ n $, $ l $, and $ m $ corresponds to one unique orbital.

Thus, there is only one orbital corresponding to the quantum numbers $ n = 3 $, $ l = 2 $, and $ m = +2 $.

Therefore, the correct answer is 1.

The following quantum numbers are possible for how many orbital(s) $n = 3$ ,$l = 2$ and $m = +2$ are possible ?

The Correct Option is A

Solution and Explanation

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