What is the effective atomic number? Calculate effective number of copper (Z=29) in \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]

Hint: There is a short name for Effective atomic number, it is EAN. By using EAN we can find the stability of the metal in coordination complexes. If EAN of any metal in coordination complex is equal to the electrons of noble gases then we can say that the particular complex is more stable.


Complete step by step solution:
The total number of electrons present with a central metal atom or ion in a coordination complex plus the electrons donated by the ligands is known as Effective Atomic Number (EAN).

The formula to calculate the EAN is as follows.
Effective atomic number = Z−O.N+2[C.N]
Z = Atomic number
O.N= Oxidation number
C.N = Coordination number
The EAN of the given complex is \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] is as follows.
The number of ligands directly attached to metal in \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] is four (coordination number).
The oxidation state of the copper in \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]is,
\[\begin{align}
  & x+4(0)=2 \\
 & x=2 \\
\end{align}\]
The oxidation state of the copper in \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] is +2.
Now we can calculate EAN of the given complex easily.
\[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]
EAN = Z−O.N+2[C.N]
EAN = 29−2+2(4)
EAN = 35.
The EAN of \[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] is 35.


Note: The number of ligands that are directly attached to metal atoms in a coordination complex is called coordination number of that particular metal. All the metal won’t have the same coordination number; it is going to depend on the number of electrons accepted by the metal which is located at the center of the coordination complex.