Question

A transition metal 'M' among Sc, Ti, V , Cr, Mn and Fe has the highest second ionisation enthalpy. The spin only magnetic moment value of M+
ion is ______ BM (Near integer) (Given atomic number Sc : 21, Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)

Answer 1

Correct Answer: 6

To determine the transition metal 'M' with the highest second ionisation enthalpy, we must compare the elements Sc, Ti, V, Cr, Mn, and Fe. Second ionisation enthalpy typically increases with a greater effective nuclear charge and less electron shielding. Among these elements, Cr (Chromium) has the highest second ionisation enthalpy due to its electronic configuration.

The electronic configuration of Cr is [Ar] 3d⁵ 4s¹. Upon losing one electron, Cr becomes Cr⁺ with the configuration [Ar] 3d⁵. The presence of a half-filled d subshell in Cr⁺ offers additional stability, contributing to a higher second ionisation enthalpy.

Now, the spin-only magnetic moment for a d⁵ configuration is calculated using the formula:
µ = √n(n + 2) BM
Where n is the number of unpaired electrons. For Cr⁺, n = 5. Thus,
µ = √5(5 + 2) = √35 ≈ 5.92 BM.
Since the question asks for the value as a near integer, we round this to 6 BM.

Therefore, the spin-only magnetic moment of the M⁺ ion is 6 BM, which lies within the expected range of 6,6.

Answer 2

To determine which transition metal 'M' has the highest second ionization enthalpy among Sc, Ti, V, Cr, Mn, and Fe, we need to analyze the electronic configurations and related properties. The second ionization enthalpy is the energy required to remove an electron from a singly charged cation (M⁺). It is typically high for elements where removing an electron significantly disrupts a stable configuration.

1. Determine the electronic configuration of each element:

• Sc (Z=21): [Ar] 3d¹ 4s²
• Ti (Z=22): [Ar] 3d² 4s²
• V (Z=23): [Ar] 3d³ 4s²
• Cr (Z=24): [Ar] 3d⁵ 4s¹
• Mn (Z=25): [Ar] 3d⁵ 4s²
• Fe (Z=26): [Ar] 3d⁶ 4s²

2. Evaluate the second ionization: Removing the second electron from M⁺.
3. Cr ([Ar] 3d⁵) has a half-filled 3d subshell, which is notably stable. Removing one more electron to form Cr²⁺ disrupts this stability, resulting in high ionization enthalpy.
Answer: Cr has the highest second ionization enthalpy.

4. Find the spin-only magnetic moment of Cr⁺ (d⁵ configuration):
The magnetic moment (µ) is given by µ=√n(n+2), where n is the number of unpaired electrons.

• Cr⁺ has 5 unpaired electrons: 3d⁵
• µ=√5(5+2)=√35 ≈ 5.92 BM

5. Verification:
The calculated magnetic moment is approximately 6 BM, which is within the given range of 6,6.

Conclusively, the spin-only magnetic moment of Cr⁺ ion is approximately 6 BM.