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How do we know that copper and chromium have different electronic configurations?

Answer
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Hint: When we do the configuration of d-block elements, then there are some exceptional configurations due to half-filled and fully-filled d-orbitals, and these configuration electrons from the s-orbital will jump to the d-orbital.

Complete answer: The electronic configuration is the arrangement of electrons in the element in the orbitals of the increasing order of the energy.
The order is:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p…….
When we do the configuration of d-block elements, then there are some exceptional configurations due to half-filled and fully-filled d-orbitals, and these configuration electrons from the s-orbital will jump to the d-orbital.
So, the given elements in the question are chromium and copper. Chromium is the element of group 6 and period 4, so its atomic number is 24. Therefore, there are 24 electrons in chromium. The electronic configuration is:
$1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{1}}3{{d}^{5}}$
This is an exceptional configuration because one electron from the 4s orbital has jumped to the 3d-orbital. After all, it will lead to extra stability of the half-filled d-orbital as there are 5 electrons in the d-orbital.
Copper is the element of group 11 and period 4, so its atomic number is 29. Therefore, there are 29 electrons in copper. The electronic configuration is:
$1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{1}}3{{d}^{10}}$
This is an exceptional configuration because one electron from the 4s orbital has jumped to the 3d-orbital. After all, it will lead to extra stability of the fully-filled d-orbital as there are 10 electrons in the d-orbital.

Note: There are many other elements that have an exceptional electronic configuration like molybdenum, ruthenium, palladium, silver, gold, platinum, roentgenium, etc.