Question

Magnetic moment of V(Z=23), Cr(Z=24), and Mn(Z=25) are x, y, z respectively, hence:
a.) x=y=z
b.) x < y < z
c.) x < z < y
d.) z < y < x

Answer 1

Hint: Electronic configuration of each element is written as magnetic moment is dependent on the number of unpaired electrons present is each element.

Complete answer:
As we know,
Magnetic moment is directly proportional to number of unpaired electrons. As its formula is:
$\mu =n\left( n+2 \right)$
Where n stands for number of unpaired electrons present in an element
So, more the number of unpaired electrons greater is the magnetic moment.
Element V has atomic number 23. The electronic configuration of vanadium is$[Ar]3{{d}^{3}}4{{s}^ {2}}$. The d-orbital has five subshell and vanadium 3 electrons are present in subshells of d-orbitals. When each subshell of d-orbital has one electron then only the pairing will start in it.
Therefore, in vanadium there is no pairing of electrons in 3d-orbital and 4s have only one subshell and it already has two electrons leaving no unpaired electron in its subshell. Hence, it contains 3 paired electrons and its magnetic moment is given by x
Element Cr has atomic number 24. The electronic configuration of chromium is$[Ar]3{{d}^{5}}4{{s}^ {1}}$. One electron of 4s moves to 3d orbital so that it can achieve a half-filled orbital stage which is in a stable state. Hence contains 6 unpaired electrons 5 in d-orbital and 1 in s-orbital and its magnetic moment is given by y
Element Mn has atomic number 25. The electronic configuration of manganese is$[Ar]3{{d}^{5}}4{{s}^ {2}}$. It has one electron in each subshell of d-orbital and 2 electrons in s-orbital. But the electrons in s-orbital are paired. Hence, it contains 5 unpaired electrons and its magnetic moment is given by z. We know that as the number of unpaired electrons increases in the element the magnetic moment also increases with it.
Therefore, numbers of unpaired electrons are more in element chromium followed by manganese and vanadium. So the magnetic moment of chromium which is represented by y would be highest followed by manganese that is represented as x and in the last would be vanadium which is given by z.

So, x < z < y

The correct option is option C.

Note: Magnetic moment is dependent on the number of unpaired electrons present in the element. They have a direct relationship between unpaired electron and magnetic moment. More the number of unpaired electrons present in an element more is the magnetic moment. Magnetic movement is the vector sum of spin and the orbital magnetic moment.