JEE Main 2024 — D And F Block Elements Question with Solution

First, we need to understand the oxidation states of chromium in the given compounds and determine their magnetic moments based on their electronic configurations.

1. $$\mathrm{CrO}$$: In $$\mathrm{CrO}$$, the oxidation state of chromium is +2. The electronic configuration of chromium (Cr) is $$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^1$$. In the +2 oxidation state, two electrons are removed, typically from the 4s and one of the 3d orbitals, leaving us with the configuration $$3d^4$$.

To find the spin-only magnetic moment, we use the formula:

$$\mu =\sqrt{n(n+2)}\mathrm{BM}$$

where n is the number of unpaired electrons. For $${\mathrm{Cr}}^{2+}$$, we have 4 unpaired electrons in the 3d orbitals.

Thus,

$$\mu =\sqrt{4(4+2)}=\sqrt{24}\approx 4.90\mathrm{BM}$$

2. $${\mathrm{Cr}}_2{\mathrm{O}}_3$$: In $${\mathrm{Cr}}_2{\mathrm{O}}_3$$, the oxidation state of chromium is +3. The electronic configuration of $${\mathrm{Cr}}^{3+}$$ is $$3d^3$$ after losing three electrons.

For $${\mathrm{Cr}}^{3+}$$, there are 3 unpaired electrons.

Thus,

$$\mu =\sqrt{3(3+2)}=\sqrt{15}\approx 3.87\mathrm{BM}$$

3. $${\mathrm{CrO}}_3$$: In $${\mathrm{CrO}}_3$$, the oxidation state of chromium is +6. The electronic configuration of $${\mathrm{Cr}}^{6+}$$ is $$3d^0$$ after losing six electrons. There are no unpaired electrons for $${\mathrm{Cr}}^{6+}$$.

Since $${\mathrm{Cr}}^{6+}$$ has no unpaired electrons, its spin-only magnetic moment is 0 BM.

The magnetic moment values for each compound are:

• $$\mathrm{CrO}$$: 4.90 BM (basic oxide)
• $${\mathrm{Cr}}_2{\mathrm{O}}_3$$: 3.87 BM (amphoteric oxide)
• $${\mathrm{CrO}}_3$$: 0 BM

The sum of the spin-only magnetic moments of the basic and amphoteric oxides is:

$$4.90+3.87=8.77\mathrm{BM}$$

Expressing in terms of $$10^{-2}\mathrm{BM}$$,

$$8.77\mathrm{BM}\times 100=877(\times 10^{-2}\mathrm{BM})$$

Thus, the sum of spin-only magnetic moment values of basic and amphoteric oxides is approximately 877 $$\times 10^{-2}\mathrm{BM}$$ (nearest integer).