The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is :

d3 (in weak as well as in strong fields)

Coordination Compounds PYQ — JEE Main 2005 · Shift 0 · Q46 with Solution

View written solutionFree

Correct answer: A

For the spin-only magnetic moment, we use

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

where $n$ is the number of unpaired electrons.

We need the configuration for which

\mu = 2.84\ \text{BM}

So,

\sqrt{n(n+2)} = 2.84

Checking small integer values of $n$ :

If $n=1$ , then $\mu=\sqrt{3}=1.73$ BM
If $n=2$ , then $\mu=\sqrt{8}=2.83$ BM
If $n=3$ , then $\mu=\sqrt{15}=3.87$ BM

Thus, $2.84$ BM corresponds to $n=2$ unpaired electrons.

Now evaluate each option.

Option A: $d^4$ in strong ligand field

For strong field, electrons pair in lower $t_{2g}$ orbitals first:

t_{2g}^4 e_g^0

Arrangement in $t_{2g}$ :

three electrons occupy singly first
fourth electron pairs in one orbital

So number of unpaired electrons = $2$ . Hence,

\mu = \sqrt{2(2+2)} = \sqrt{8} = 2.83 \approx 2.84\ \text{BM}

So A is correct.

Option B: $d^4$ in weak ligand field

For weak field, high-spin configuration:

t_{2g}^3 e_g^1

Unpaired electrons = $4$ . Thus,

\mu = \sqrt{4(4+2)} = \sqrt{24} = 4.90\ \text{BM}

So B is incorrect.

Option C: $d^3$ in weak as well as strong fields

Configuration:

t_{2g}^3 e_g^0

Unpaired electrons = $3$ in both cases. Thus,

\mu = \sqrt{3(3+2)} = \sqrt{15} = 3.87\ \text{BM}

So C is incorrect.

Option D: $d^5$ in strong ligand field

Strong field gives low-spin configuration:

t_{2g}^5 e_g^0

Unpaired electrons = $1$ . Thus,

\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.73\ \text{BM}

So D is incorrect.

Therefore, the only configuration with spin-only magnetic moment $\approx 2.84$ BM is:

\boxed{\text{A: } d^4 \text{ (in strong ligand field)}}

Comparison with stored correct answer:

Stored correct answer: A
Derived answer: A

They agree.

More from Coordination Compounds

View written solutionFree

Correct answer: A

For the spin-only magnetic moment, we use

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

where $n$ is the number of unpaired electrons.

We need the configuration for which

\mu = 2.84\ \text{BM}

So,

\sqrt{n(n+2)} = 2.84

Checking small integer values of $n$ :

If $n=1$ , then $\mu=\sqrt{3}=1.73$ BM
If $n=2$ , then $\mu=\sqrt{8}=2.83$ BM
If $n=3$ , then $\mu=\sqrt{15}=3.87$ BM

Thus, $2.84$ BM corresponds to $n=2$ unpaired electrons.

Now evaluate each option.

Option A: $d^4$ in strong ligand field

For strong field, electrons pair in lower $t_{2g}$ orbitals first:

t_{2g}^4 e_g^0

Arrangement in $t_{2g}$ :

three electrons occupy singly first
fourth electron pairs in one orbital

So number of unpaired electrons = $2$ . Hence,

\mu = \sqrt{2(2+2)} = \sqrt{8} = 2.83 \approx 2.84\ \text{BM}

So A is correct.

Option B: $d^4$ in weak ligand field

For weak field, high-spin configuration:

t_{2g}^3 e_g^1

Unpaired electrons = $4$ . Thus,

\mu = \sqrt{4(4+2)} = \sqrt{24} = 4.90\ \text{BM}

So B is incorrect.

Option C: $d^3$ in weak as well as strong fields

Configuration:

t_{2g}^3 e_g^0

Unpaired electrons = $3$ in both cases. Thus,

\mu = \sqrt{3(3+2)} = \sqrt{15} = 3.87\ \text{BM}

So C is incorrect.

Option D: $d^5$ in strong ligand field

Strong field gives low-spin configuration:

t_{2g}^5 e_g^0

Unpaired electrons = $1$ . Thus,

\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.73\ \text{BM}

So D is incorrect.

Therefore, the only configuration with spin-only magnetic moment $\approx 2.84$ BM is:

\boxed{\text{A: } d^4 \text{ (in strong ligand field)}}

Comparison with stored correct answer:

Stored correct answer: A
Derived answer: A

They agree.

Coordination Compounds question

Coordination Compounds question

Option A: $d^4$ in strong ligand field

Option B: $d^4$ in weak ligand field

Option C: $d^3$ in weak as well as strong fields

Option D: $d^5$ in strong ligand field

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Coordination Compounds question

Coordination Compounds question

Option A: $d^4$ in strong ligand field

Option B: $d^4$ in weak ligand field

Option C: $d^3$ in weak as well as strong fields

Option D: $d^5$ in strong ligand field

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Option A: d4d^4d4 in strong ligand field

Option B: d4d^4d4 in weak ligand field

Option C: d3d^3d3 in weak as well as strong fields

Option D: d5d^5d5 in strong ligand field

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Option A: d4d^4d4 in strong ligand field

Option B: d4d^4d4 in weak ligand field

Option C: d3d^3d3 in weak as well as strong fields

Option D: d5d^5d5 in strong ligand field

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Option A: $d^4$ in strong ligand field

Option B: $d^4$ in weak ligand field

Option C: $d^3$ in weak as well as strong fields

Option D: $d^5$ in strong ligand field

Option A: $d^4$ in strong ligand field

Option B: $d^4$ in weak ligand field

Option C: $d^3$ in weak as well as strong fields

Option D: $d^5$ in strong ligand field