According to uncertainty principle,
\(\triangle x.m\triangle v={h\over 4\pi}\) or \(\triangle v={h\over 4\pi m \triangle x};\) h = 6.626 x 10^-34 kg m² s^-1;m = 10g = 10^-2 kg
\(\triangle x =10^{-5}m;\triangle v ={(6.626\times 10^{-.34}kgm^2s^{-1})\over4\times 3.143\times (10^{-2}kg)\times (10^{-5}m)}=5.27\times 10^{-28}\)mv

Let the no. of electrons in the ion = x
\(\therefore\) the no. of the protons = x + 3 (as the ion has three units positive charge) and the no. of neutrons = \(x+{30.4x\over 100}=x+0.304x\)
Now, mass number of ion = Number of protons + Number of neutrons
= (x + 3) + (x + 0.304 x)
\(\therefore\) 56 = (x + 3) + (x + 0.304 x) or 2.304 x = 56 - 3 = 53
\(x={53\over 2.304}=23\)
Atomic number of the ion (or element) = 23 + 3 = 26
The element with atomic number 26 is iron (Fe) and the corresponding ion is Fe³⁺.

Electronic configuration of Fe³⁺ 1s²2s²2p⁶3s²3p⁶3d⁶4s²

Electronic configuration of mn²⁺ is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵
Five unpaired electrons
Electronic configuration of Ar is 1s² 2s² 2p⁶ 3s² 3p⁶ 
no unpaired electrons.

(i) The energy of photon is sufficient to disturb a sub-atomic particle so that there is uncertainty in the measurement of position and momentum of the sub-atomic particle.
(ii) However, the energy is insufficient to disturb a macroscopic object.

From de Broglie equation, wavelength \(\lambda =\frac { h }{ mv } \)
For same wavelength with two different particles, (ie) electron and proton m₁v₁ = m₂v₂ (h is constant) Lesser the mass of the particle, greater will be the velocity.
Hence electron will have higher velocity

The solution to Schrodinger equation gives the permitted total energy values called eigen values and the corresponding wave function represent atomic orbitals.

Limitation of Bohr's atom model:
(a) The Bohr's atom model is applicable only to species having one electron such as hydrogen, Li²⁺ etc ... and not applicable to multi electron atoms.
(b) It was unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect).
(c) Bohr's theory was unable to explain why the electron is restricted to revolve around the nucleus in a fixed orbit in which the angular momentum of the electron is equal to nh/2π

Applying Bohr's postulates to a hydrogen like atom (one electron species such as H, He⁺ and Li²⁺ etc...)the radius of the n^th orbit and the energy of the electron revolving in the n^th orbit were derived. The results are as follows:
r_n = \(\frac { (0.529){ n }^{ 2 } }{ x } \mathring { A } \)  ...(1)
E_n = \(\frac { -13.6({ z }^{ 2 }) }{ { n }^{ 2 } } ev\quad { atom }^{ -1 }\)   or ...  (2) or
E_n = \(\frac { (-1312.8){ z }^{ 2 } }{ { n }^{ 2 } } kJ\quad { mol }^{ -1 }\) .....(3)

n = 4 l = 0,1,2,3
4 sub shells s, p, d & f.
I = 0 m₁ = 0 + one 4s orbital.
I = 1 m₁ = -1, 0, + 1 \(\Rightarrow\) three 4p orbitals.
I = 2 m₁ = -2,:1, 0, +1, +2 \(\Rightarrow\) five 4d orbitals.
I = 3 m₁ = -3, -2, -1,0, +1, +2, +3 \(\Rightarrow\) seven 4f orbitals.
Over all 16 orbitals are possible.

(i) Atoms consist of huge positively charged centers called nuclei.
(ii) Most of the space inside the atom is empty.

According to this theory, atom was assumed to consist of a sphere of uniform distribution of about 10^-10 m positive charge with electrons embedded in it such that the number of electrons equal to the number of positive charges and the atom as a whole is electrically neutral.

Energy electrons symmetry
This is due to the symmetrical distribution and exchange energy of given d- electrons. Symmetry leads to stability.
Exchange energy:
If two or more electrons with the same spin are present in degenerate orbitals, there is a possibility for exchanging their positions. During exchange process, the energy is released and the released energy is called exchange energy. If more number of exchanges are possible, more exchange energy in released. More number of exchanges are possible only in case of half filled and fully filled configurations.
For example, in chromium the electronic configuration is [Ar]3d⁵ 4s¹. The 3d orbital is half filled and there are ten possible exchanges as shown in figure. On the other hand only six exchanges are possible for [Ar]3d⁴ 4s² configuration. Hence, exchange energy for the half filled configuration is more. This increases the stability of half filled 3d orbitals.

The exchange energy is the basis for Hund's rule, which allows maximum multiplicity, that is electron pairing is possible only when all the degenerate orbitals contain one electron each.