1. Why is +2 oxidation state of Mn (25) quite stable, while the s… - Vidyadip

Question

Why is $+2$ oxidation state of Mn (25) quite stable, while the same is not true for iron (26)?
What is meant by dual nature of electrons? Calculate the energy and wavelength of the photon emitted by hydrogen atom when electron makes a transition from $n = 2$ to $n = 1$. Given that the ionisation potential is $13.6 eV. (1eV = 1.6 \times 10^{-19}J)$.

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Answer

$Mn^{2+}(25): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^0 3d^5$

$Mn^{2+}$ is more stable due to half filled d-orbitals.
$Fe^{2+}(26): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^0 3d^6$
$Fe^{2+}$ is not stable because it does not have half filled d-orbitals.

Dual nature of electrons means electron is associated with both particle and wave like nature.

$\Delta\text{E}=-13.6\text{eV}\frac{1}{\text{n}^2_1}-\frac{1}{\text{n}^2_2}$
$=-13.6\text{eV}\frac{1}{2^2}-\frac{1}{1^2}$
$=-13.6\Big(-\frac{3}{4}\Big)=10.2\text{eV}$
$\Delta\text{E}=10.2\times1.6\times10^{-19}\text{J}$
$=16.32\times10^{-19}\text{J}=1.632\times10^{-18}\text{J}$
$\Delta\text{E}=\frac{\text{hc}}{\lambda}$
$\lambda=\frac{\text{hc}}{\lambda}=\frac{6.626\times10^{-34}\text{Js}\times3\times10^8}{16.32\times10^{-19}}$
$=1.22\times10^{-7}\text{m}=122\text{nm}$

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