Some species are given

Ni²⁺, Fe²⁺, Co²⁺, V³⁺ and Ti²⁺

How many species has magnetic moment (spin only) less than 3 BM.

The correct answer is 3.

To determine how many of the given species have a spin-only magnetic moment less than 3 BM, we need to calculate the number of unpaired electrons for each transition metal ion.

The spin-only magnetic moment (${\mu }_s$) is given by the formula:

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

where $n$ is the number of unpaired electrons.
For ${\mu }_s$ to be less than 3 BM, the value of $n$ must be less than 3 (since for $n=3$, ${\mu }_s=\sqrt{3(3+2)}=\sqrt{15}\approx 3.87\text{BM}$). Therefore, we are looking for species with $n<3$, i.e., $n=1$ or $n=2$.

Let us analyze the valence shell electron configuration and count the number of unpaired electrons ($n$) for each ion:

1. Ni²⁺ (Titanium to Nickel series, Z = 28):
Electronic configuration of Ni: [Ar] 3d⁸ 4s²
Electronic configuration of Ni²⁺: [Ar] 3d⁸
Number of unpaired electrons ($n$) = 2
${\mu }_s=\sqrt{2(2+2)}=\sqrt{8}\approx 2.83\text{BM}$ (which is < 3 BM).

2. Fe²⁺ (Z = 26):
Electronic configuration of Fe: [Ar] 3d⁶ 4s²
Electronic configuration of Fe²⁺: [Ar] 3d⁶
Number of unpaired electrons ($n$) = 4
${\mu }_s=\sqrt{4(4+2)}=\sqrt{24}\approx 4.90\text{BM}$ (which is > 3 BM).

3. Co²⁺ (Z = 27):
Electronic configuration of Co: [Ar] 3d⁷ 4s²
Electronic configuration of Co²⁺: [Ar] 3d⁷
Number of unpaired electrons ($n$) = 3
${\mu }_s=\sqrt{3(3+2)}=\sqrt{15}\approx 3.87\text{BM}$ (which is > 3 BM).

4. V³⁺ (Z = 23):
Electronic configuration of V: [Ar] 3d³ 4s²
Electronic configuration of V³⁺: [Ar] 3d²
Number of unpaired electrons ($n$) = 2
${\mu }_s=\sqrt{2(2+2)}=\sqrt{8}\approx 2.83\text{BM}$ (which is < 3 BM).

5. Ti²⁺ (Z = 22):
Electronic configuration of Ti: [Ar] 3d² 4s²
Electronic configuration of Ti²⁺: [Ar] 3d²
Number of unpaired electrons ($n$) = 2
${\mu }_s=\sqrt{2(2+2)}=\sqrt{8}\approx 2.83\text{BM}$ (which is < 3 BM).

Thus, the species having a magnetic moment less than 3 BM are Ni²⁺, V³⁺, and Ti²⁺.

Therefore, there are 3 such species.