Question

the following quantum number are possible for how many orbitals:n=3 l=2 m=+2

Answer 1

n = 3; l = 2 and m = +2 represents one of the 3d orbital with magnetic quantum number +2.

No two orbitals have same magnetic quantum number. Hence the given quantum number is possible for only one orbital and two electrons.

Answer 2

The following quantum numbers are possible for one orbital.

• There are four quantum numbers- n, l, m, and s
• n, which is the principal quantum number. Its value denotes the shell.
• l, is the azimuthal quantum number. Its value is 0 to n-1.
• l is 0,1,2,3 for s, p, d, and f -subshells respectively.
• s is the spin quantum number, it can be +1/2 or -1/2
• m is the magnetic quantum number, its value is -l to +l.

• As per question, for n = 3, l = 2, m = +2, there will be one orbital 3dx²-dy² orbital of d-subshell.
• Because, as its n =2, and l = 2 that means it belongs to the 3d-subshell.
• And, a d-subshell has 5 orbitals that are dxy, dyz, dxz, dx²-dy², and dz².
• m = -2, -1, 0, +1, +2 for dxy, dyz, dxz, dz², and dx²-dy²  respectively.
• As, m = +2 is the value for 3dx²-dy² orbital.
• Therefore, for n =3, l =2, m = +2, there is only one orbital i.e. 3dx²-dy² orbital.