# compare and contrast a 2p6 orbital to a 4s1 using quantum numbers to help [closed]

Would you be able to help me understand how to compare and contrast a 2p6 orbital to a 4s1 using quantum numbers to help?

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$$2\mathrm{p}^6$$, $$4\mathrm{p}^1$$ are not orbitals.

It is a partial description of an atom electron configuration, saying there are 6 electrons in 3 orbitals $$2\mathrm{p}$$, respectively 1 electron in the orbital $$4\mathrm{s}$$.

$$2$$ in $$2\mathrm{p}$$ means the (main, energy ) quantum number $$n=2$$. $$n$$ can have values 1, 2, .....

$$p$$ in $$2\mathrm{p}$$ means the ( orbital, orbital angular momentum) quantum number $$\ell=1$$. $$\ell$$ can have values 0, 1, ... , $$n$$ - 1.

The ( magnetic ) quantum number $$m$$ ( $$-\ell \le m \le +\ell$$ ) is for the axis projection of the vector of the electron orbital momentum ), determining e.g. there is

• 1 orbital $$n\mathrm{s}$$

• 3 orbitals $$n\mathrm{p}$$, called $$\mathrm{p_x, p_y,p_z}$$

• 5 orbitals $$n\mathrm{d}$$, called $$\mathrm{d_{{xy}^2}, d_{{xz}^2}, d_{{yz}^2}, d_{x^2-y^2}, d_{z^2}}$$

• 7 orbitals $$n\mathrm{f}$$, being seldom explicitly named.

In a hydrogen atom, or ions with just 1 electrons, orbitals with the same $$n$$ have the same energy(*).

In multielectron atoms, electrons in different orbitals have different interaction with other electrons and their energy differ. Their energy increases in order $$\mathrm{s < p < d < f}$$

Generally, but with multi exceptions, the energy ( and filling order) increases in this order:

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 4d 7p

The naming has historical origin in spectroscopy. s as sharp, p as principal, d as diffuse, f as fundamental.

1. s means $$\ell = 0$$
2. p means $$\ell = 1$$
3. d means $$\ell = 2$$
4. f means $$\ell = 3$$

Orbitals have 3 meanings:

1. A wave function being a particular solution of the Schroedinger wave equation, with integer constants $$n, l, m$$ called quantum numbers.
2. An electron quantum state with the particular $$n, l, m$$ values
3. A 3D shape, describing the probable electron occurence, with borders defined by occurence probability threshold, corresponding to 1 and 2.

(*) Relativistic corrections for Schroedinger equation reveals and explain observations it is not fully true.