The oxidation states displayed by the first half of the first row of transition metals are given in the table below
| Oxidation state | Sc | Ti | V | Cr | Mn |
| +2 | +2 | +2 | +2 | ||
| +3 | +3 | +3 | +3 | +3 | |
| +4 | +4 | +4 | +4 | ||
| +5 | +5 | +6 | |||
| +6 | +7 |
It can be easily observed that except Sc, all others metals display +2 oxidation state. Also, on moving from Sc to Mn, the atomic number increases from 21 to 25. This means the number of electrons in the 3d-orbital also increases from 1 to 5.
Sc (+2) = d1
Ti (+2) = d2
V (+2) = d3
Cr (+2) = d4
Mn (+2) = d5
+2 oxidation state is attained by the loss of the two 4selectrons by these metals. Since the number of delectrons in
(+2) state also increases from Ti(+2) to Mn(+ 2), the stability of +2 state increases (as d-orbital is becoming more and
more half-filled). Mn (+2) has d 5electrons (that is half-filled dshell, which is highly stable).
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).
