Question

How many orbitals are described by each of the below combinations of quantum numbers? 

n= 3, l =0 

_______ orbitals 

n=4, l = 2, ml = 2 

_______ orbitals

Answer 1

The numbers which gives complete information of electrons such as position, energy,... are called Quantum numbers.

There are 4 quantum numbers.

1.Principal Quantum Number: 1. This is proposed by Bohr. 2. It is denoted by "n" 3. It has values 1,2,3,4..... 4) It gives energy of the electron and size of the orbit.

2. Azimuthal quantum number or Angular momentum quantum number:

i) It is proposed by Somerfield ii) It is denoted by l

iii) It has values from 0,1,2,3....(n-1).

iv) It gives the shape of the orbital and number of sub-shells present in a main shell.

If l = 0, it is a S-orbital. If l = 1, it is a p-orbital. If l = 2, it is a d - orbital.

3) Magnetic quantum number: i) It is proposed by Lande. It is denoted by m. It has values from-l......0......+l, a total of (2l+1) m values. It gives orientation of orbital in space.

4) Spin quantum number: It is proposed by Ullenbeck and Goudsmith. It is denoted by "s". It gives spin of the electron.

n = 3 & l = 0 corresponds to 3S orbital.

n = 3 corresponds to main shell. l = 0 corresponds to azimuthal quantum number which signifies the sub-shell present in a main shell.

n = 3 & l = 0 corresponds to One orbital ie 3S orbital

2)

n = 4, l = 2, m​​​​​​l = 2 corresponds to 4dxy or 4dyz or 4dxz or 4dx2-y2 or 4dz2 orbital. All these 5 orbitals are degenerate orbitals ie having same energy.

It is also corresponds to only one orbital. It corresponds to either of one of the orbitals mentioned above.