Confusion regarding orbital, electron and Quantum no’s [closed]

Question

Now , In some textbook I have read that orbital is nothing but the shape of electron . s,p,d orbitals etc.

So , after knowing shape of an orbital . I got to know that inside the orbital is an electron and there is a probability of electron to be present in it at specific positions( So , please confirm me if we talk about only one electron inside any one orbital ).

Now , the i am getting infused from textbook after reading that azimuthal Q number does not talk shape of electron but talks about shape of orbital .

Now , it is because I also read that shape of an electron is same as shape of an orbital.

Also , L quantum number tells about at which place the probability electron is 0. That’s what L values tell us .

Does it also tell about shape of orbital ? Also , how does it tell us about sub energy level .

What do these lines here represent.

Please help me in correct here.

Answer 1

The atomic orbital is a mathematical model that tries to explain the behaviour of electrons around the nucleus of an atom. Like any other theory explaining the behaviours of sub-atomic particles, this is purely based on experimental data and mathematics. No one has actually seen how an electron looks like because it is simply not possible to 'see' sub-atomic particles like one might see cells of living organisms under a microscope.

The atomic orbitals are mathematical functions based on the theories and assumptions of the Wave Mechanic model of the atom.

Each atomic orbital features a set of unique values namely Principal Quantum Number ($n$), Azimuthal Quantum Number ($l$) and Magnetic Quantum Number ($m_l$).

The job of each of these quantum numbers is to give you information about the energy (you can estimate the position of the electron relative to the nucleus from this), angular momentum (you can estimate the region in which the probability of finding the electron is highest, and thus the 'shape of the orbital' from this) and magnetic moment of the electron, respectively.

All of these together - $n$, $l$ and $m_l$ (along with the Spin Magnetic Quantum number, $m_s$) give the unique quantum state of an electron. This is called its orbital. And according to Pauli's Exclusion Principle, no two electrons can have the same orbitals (the same value for all the four quantum numbers).

It is impossible to determine the actual shape of an electron. But, we can make mathematical models that help understand their behaviour and maybe use those to our benefits. Atomic orbitals or even the concept of electrons for that matter are mathematical models for explaining the experimental data.

Answer 2

An orbital is the region of space, in which an electron has a probability at least of 95% be present. The quantum numbers give the following information:

• $n$ is the principal quantum number and it is responsible of the extension of an orbital (a 2s orbital is bigger than a 1s orbital)
• $l$ is the secondary quantum number (Clebsh-Gordan series $l=0, \dots, n-1$) and it gives the shape of the orbital ($l=0$ implies a sphere)
• $m$ is the magnetic quantum number and it gives the orientation of the orbital $m=-l, \dots, l$

Please, read some textbooks like the Atkins' Physical Chemistry.