નીચે આપેલા આયનોમાંથી કયાની 'સ્પીન ફકત' ચુંબકીય ચાકમાત્રા સમાન છે? \(A\). \(\mathrm{Ti}^{3+}\) \(B\). \(\mathrm{Cr}^{2+}\) \(C\). \(\mathrm{Mn}^{2+}\) \(D\).\(\mathrm{Fe}^{2+}\) \(E\). \(\mathrm{Sc}^{3+}\) નીચે આપેલા વિકલ્પોમાંથી સૌથી બંધબેસતો જવાબ પસંદ કરો.

A ફ્ક્ત \(A\) અને \(E\)
B ફ્ક્ત \(B\) અને \(C\)
C ફ્ક્ત \(A\) અને \(D\)
D ફ્ક્ત \(B\) અને \(D\)

Verified Solution

Answer & Solution

Correct Answer

(D) ફ્ક્ત \(B\) અને \(D\)

Step-by-step Solution

Detailed explanation

lons	No. of unpaired electrons	Configuration
\( \mathrm{Ti}^{3+} \)	\(1\)	\(3 d^1\)
\( \mathrm{Cr}^{2+} \)	\(4\)	\(3 d^4\)
\( \mathrm{Mn}^{2+} \)	\(5\)	\(3 d^5\)
\( \mathrm{Fe}^{2+} \)	\(4\)	\(3 d^6\)
\( \mathrm{Sc}^{3+}\)	\(0\)	\(3 d^0\)

Spin only magnetic moment is given by \(\sqrt{n(n+2)} \mathrm{BM}\) \(\therefore \mathrm{Cr}^{2+}\) and \(\mathrm{Fe}^{2+}\) will have same spin only magnetic moment.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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સૂચિ-I (ક્વોન્ટમ આંક)			સૂચિ-II (કક્ષક)
	'n'	'l'
(A)	2	1	(I) 3d
(B)	4	0	(II) 2p
(C)	5	3	(III) 4s
(D)	3	2	(IV) 5f