It states that electron pairing in the degenerate orbitals does not take place until all the available orbitals contain one electron each.

The energy of the 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium and that of lithium is greater than that of sodium and so on because H (Z = 1), Li (Z = 3) and Na (Z = 11). When atomic number increases, the energies of the same orbital decreases.
E_2s(H) > E_2s(Li) > E_2s(Na) > E_2s(K) ..............

Shape of s-orbital - sphere
Shape of p-orbital- dumb bell
Shape of d-orbital- clover leaf

As we know there are three different orientations in space that are possible for a p orbital. All the three p orbitals, namely, px, py and pz have same energies and are called degenerate orbitals. However, in the presence of magnetic or electric field the degeneracy is lost.

\(E_n={(-1312.8)Z^2\over n^2}KJ\ mol^{-1}\)
Where Z = atomic number, n = principal quantum number.

For 4p orbital: Number of angular nodes = l
For 4p orbital l = 1
\(\therefore\) Number of angular nodes = 1
Number of radial nodes = n - l - 1
= 4-1-1
= 2
\(\therefore\)Total number of nodes = n -1 = 4 - 1 = 3
1 angular node and 2 radial nodes.
For 4d orbital: Number of angular nodes = 1
For 4d orbital 1= 2
\(\therefore\) Number of angular nodes = 2,
Number of radial nodes = n - l- 1
=4-2-1
= 1
\(\therefore\) Total number of nodes = n - 1 = 4 - 1 = 3
1 radial nodes and 2 angular node.

(i) The region where there is probability density function reduces to zero is called nodal surface or a radial node.
(ii) For ns orbital, (n -1) nodes are found in it.

(i) \(\psi\) itself has no physical meaning but it represents an atomic orbital.
(ii) \(\psi^2\) is related to the probability of finding the electrons within a given volume of space.

n = 3, main shell is m.
Total number of orbitals in 3rd energy level =?

Total number of orbitals = 9.

(i) \(\lambda =\frac{h}{mv}\). This equation implies that a moving particle can be considered as a wave and a wave can exhibit the properties of a particle.
(ii) For a particle with high linear momentum (mv) the wavelength will be so small and cannot be observed.
(iii) For a microscopic particle such as an electron, the mass is of the order of 10^-31 kg, hence the wavelength is much larger than the size of atom and it becomes significant.
(iv) For the electron, the de Broglie wavelength is significant and measurable while for the iron ball it is too small to measure, hence it becomes insignificant.

(i) Albert Einstein proposed that light has dual nature. i.e. like photons behave both like a particle and as a wave.
(ii) Louis de Broglie extended this concept and proposed that all forms of matter showed dual character.
(iii) He combined the following two equations of energy of which one represents wave character (hv) and the other represents the particle nature (mc²).

(i) The theory of electromagnetic radiation states that a moving charged particle should continuously loose its energy in the form of radiation.
(ii) Therefore, the moving electron in an atom should continuously loose its energy and finally collide with nucleus resulting in the collapse of the atom.

J. J. Thomson's cathode ray experiment revealed that atoms consist of negatively charged particles called electrons. He proposed that atom is a positively,charged sphere in which the electrons are embedded like the seeds in the watermelon.

Copper (Z = 29)
Expected configuration: 1S²2s² 2p⁶ 3s² 3p⁶ 3d⁹ 4s²
Actual configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s¹
The reason is that fully filled orbitals have been found to have extra stability.
Copper has the electronic configuration [Ar] 3d ¹⁰ 4s ¹ and not [Ar] 3d⁹ 4s² due the symmetrical distribution and exchange energies of d electrons.
Symmetry leads to stability. The full filled configuration have symmetrical distribution of electrons and hence they are more stable than unsymmetrical configuration.

Cr (Z = 24) 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹.
The reason for this is, Cr with 3d⁵ configuration is half filled and it will be more stable.
Chromium has [Ar] 3d⁵ 4s¹ and not [Ar] 3d⁴ 4s² due to the symmetrical distribution and exchange energies of d electrons.

The distribution of electrons into various orbitals of an atom is called its electronic configuration.
N (Z = 7)
 

(i) Cr (Z = 24) Is² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹
Cr³⁺ - Is² 2s² 2p⁶ 3s² 3p⁶ 3d⁴.
It contains 4 unpaired electrons.
(ii) Ne (Z = 10) 1s²2s² 2p⁶. No unpaired electrons in it.