Term Symbol MCQ Quiz in मराठी - Objective Question with Answer for Term Symbol - मोफत PDF डाउनलोड करा

CONCEPT:

Term Symbols and Electronic Configurations

• The term symbol gives information about the quantum states of electrons in atoms, including their spin and orbital angular momentum.
• Term symbols take the form: \(^{2S+1}L_J \)
• Where:
  • S is the total spin quantum number.
  • L is the total orbital angular momentum, represented by a letter (S=0, P=1, D=2, F=3, etc.).
  • J is the total angular momentum quantum number (resultant of L and S).

EXPLANATION:

• For the electronic configuration of Be: 1s² 2s¹ 3s¹, we only consider the valence electrons (2s¹ 3s¹).
• Each s orbital electron has an orbital angular momentum quantum number l = 0 .
• Total orbital angular momentum L :
  • \(L (total) = l_1 + l_2 = 0 + 0 = 0\)
• Each s orbital electron has a spin quantum number s =\( \pm \frac{1}{2}\) .
• Total spin angular momentum S :
  • \(S (total) = s_1 + s_2 = \frac{1}{2} + \frac{1}{2} = 1\)
• Multiplicity (2S + 1):
  • Multiplicity = 2S + 1 = 2(1) + 1 = 3
• Given that L = 0 (S term) and S = 1, the term symbol must account for:
  • J = L + S = 0 + 1 = 1

Therefore, the term symbol for the first excited state of Be with the electronic configuration 1s²2s¹3s¹ is 3S₁.

- Correct Option: 3) 5E

- Solution Statement:
- The ground Mundefinedlliken symbol of the central metal ion in the complex \([FeCl_4]^{2-}\) is represented as 5E. This symbol indicates the electronic configuration and the term symbol of the lowest energy state (ground state) of the iron ion in the given complex.

- Overview of Incorrect Options:
- 1) 5D: This option suggests a d-d electronic configuration with a term symbol of 5D, which is not applicable for the \([FeCl_4]^{2-}\) complex as it does not accurately represent the ground state of the iron ion in this specific ligand field environment.
- 2) 5Eg: The "g" subscript refers to gerade or symmetric with respect to inversion through the center of the molecule, typically used in octahedral complexes. However, the term symbol alone without "g" is the correct notation for the ground state of the iron ion in the given tetrahedral complex.
- 4) 6S: This option suggests a term symbol that would be applicable for a high-spin d^6 configuration under a weak field, but it does not correctly represent the ground state of iron in the \([FeCl_4]^{2-}\) complex.

- Additional Insights:
- The term symbol 5E accurately reflects the electronic configuration and symmetry properties of the iron ion in the tetrahedral field created by the four chloride ligands. In the context of crystal field theory, the specific splitting and occupancy of d-orbitals in a tetrahedral field are different from those in an octahedral field, leading to a distinct ground state term symbol.
- The absence of "g" in the term symbol is indicative of the fact that tetrahedral complexes do not have a center of symmetry, differentiating it from octahedral complexes which often use "g" or "u" (ungerade) to indicate symmetry properties.
- The ground state term symbol is crucial for understanding the magnetic and spectroscopic properties of the complex, as well as predicting its reactivity and interaction with electromagnetic radiation.

The correct answer is A1g, Eg , T1g, T2g

Concept:-

• Group Theory and Term Symbols: Group theory aids in understanding the symmetries of molecules and complexes. Term symbols, derived using group theory, encode the symmetry properties and degeneracy of electronic states. They are crucial in predicting the behavior of complexes under various physical processes, like electronic transitions.
• Octahedral Ligand Field Splitting: In an octahedral complex, the d orbitals split into two sets due to the electrostatic field created by the surrounding ligands. The (E_g) orbitals (higher energy) and (T_{2g}) orbitals (lower energy) splitting is a fundamental concept explaining the electronic structure and properties of octahedral complexes.
• Degeneracy and Electronic States: The degeneracy of a term symbol refers to the number of states that have the same energy. In octahedral complexes, (Eg) and (T_2g) reflect the splitting and degeneracy of the d orbitals, influencing properties like color and magnetism.

Explanation:-

- In an octahedral ligand field, the term symbols represent the states that arise from the splitting of the d orbitals under the influence of the ligands surrounding the central metal ion.
- A1g represents a spherically symmetric state, which is non-degenerate (single state).
- Eg represents a doubly degenerate state, which arises from the d-orbitals that point directly at the ligands in an octahedral complex \((dz^2 \ \ and \ \ dx^2-y^2)\).
- T1g and T2g represent triply degenerate states. T2g arises from the d-orbitals (dxy, dxz, d_yz) that are between the ligands, and T1g could represent excited states or states involving orbital mixing in more complex scenarios.
- These symbols (A1g, Eg, T1g, T2g) are consistent with the possible terms in an octahedral field considering the symmetry and degeneracy of the d-orbital splitting.

Spectroscopic term	Mulliken symbol in an octahedral field
S	A1g
P	T1g
D	Eg + T2g
F	A2g + T1g + T2g
G	A1g+ Eg + T1g +T2g

Conclusion:-

So, Mülliken symbol(s) possible for ‘G’ term in octahedral ligand field is/are A1g, Eg , T1g, T2g

The correct answer is [Cr(H2O)6]2+

Concept:-

• Ground Term Symbol: This is a notation that summarizes the electronic state of a transition metal ion in a complex. It includes information on the overall spin state (multiplicity) and the distribution of electrons in orbitals (symmetry). For transition metal complexes, symbols like ⁵D help in predicting magnetic properties and the color of the complex.
• High-Spin and Low-Spin Configurations: The strength of the ligand field influences whether an electron configuration will be high-spin or low-spin. High-spin states occur when electrons tend to occupy higher energy orbitals to maximize spin, while low-spin states are a result of electrons pairing up in lower energy orbitals to minimize repulsion in strong ligand fields.

Explanation:-

- Chromium in the complex [Cr(H₂O)₆]²⁺ is in the +2 oxidation state. This means the electronic configuration of Cr²⁺ is [Ar]3d⁴.

S = +1/2+1/2+1/2+1/2= 2

SM= 2S+1= 2*2 + 1 = 5

L = =+2+1+0-1 = 2 means D
- According to Hund's rule and the distribution of electrons in d-orbitals, the ground term symbol for Cr²⁺ in this configuration is ⁵D, which arises from the highest multiplicity (2S+1=5, where S is the total spin) among the possible configurations of four electrons in five d-orbitals.
- The 5D term symbol indicates a quintet state, reflecting the high spin configuration of Cr²⁺ in this octahedral complex.

Conclusion:-

So, A complex that possess 5D ground term symbol for its metal ion is  [Cr(H2O)6]2+

The Correct Answer is ⁶S, ⁴F and ²D.

Concept:-

Ground State Term- These are the microstates occur due to j-j coupling and have the same energy when electron repulsion are taken into account, spectroscopically distinguishable energy levels are obtained called Terms. 

Ground State Term= ^2S+1L, where S= Total Spin Quantum Number and "L" is Total Orbital Quantum Number.

2S+1 is Spin Multiplicity and 

Symbols for L= 0,1,2,3,4,5 is S,P,D,F,G,H respectively

Explanation:-

Mn²⁺ = d⁵

S = 5/2, L= \(\sum{M_l}\) = 0→ S Term

(2S+1) = 6

Term Symbol = ^2S+1L = ⁶S

Similarly Cr⁺³(d³) and Cu⁺²(d⁹) shows ⁴F and ²D.

Conclusion:-

The spectroscopic ground state term symbols for the octahedral aqua complexes of Mn(II), Cr(III) and Cu(II), respectively, are ⁶S, ⁴F and ²D.

The Correct Answer is \(^3 \sum_u^+\)

Concept:-

Molecular Term symbol is represented by: ^2S+1L.

where, S is spin quantum number and L is total angular momentum quantum number.

L=0, 1, 2 & 3 is symbolises by \(\sum,\ \pi,\ \Delta,\ \phi\)  respectively.

Subscript u or g is used to describe the symmetry, where

g is Gerade Orbital, Gerade orbitals are symmetric with respect to inversion through the center of symmetry of the molecule and

u is Ungerade Orbital, Ungerade orbitals are anti-symmetric with respect to inversion through the center of symmetry of the molecule.

\(g\times u\ =\ u\\u\times u\ =\ g\\g\times g\ =\ g\)

Explanation:-

First excited state of hydrogen molecule: 

L = 0 = \(\sum\)

S = 1, 2S + 1 = 3

\(g\times u\ =\ u\)

\(=\ ^3 \sum_u^+\), for half filled orbital.

Conclusion:-

The first excited state of hydrogen molecule is \(^3 \sum_u^+\)

Concept:

• A microstate is a specific way in which we can arrange the energy of the system.
• The atomic term symbol for a particular electronic configuration is 2S+1LJ. Where 2S+1 is the spin multiplicity, L is the total orbital angular momentum and J is the total angular momentum.
• For calculating the number of microstates for a particular term symbol, we need to know the values of L and S:

L = total orbital angular momentum quantum number associated with the collection of microstates with L, and
S = total spin angular momentum quantum number associated with the collection of microstates with S.

• There are 2L+1 possible orientations of L and 2S+1 possible orientations of S, therefore, the total number of microstates in one term given L and S will be

=(2L + 1) × (2S + 1)

Explanation:-

The calculation of microstates of the given term is shown below.

For ³F term:

2S + 1 = 3

and L = 3

Therefore, 2L + 1 = 2× 3 + 1 = 7

Number of microstates are = (2S+1)(2L+1)

3× 7 = 21. 

Conclusion:-

Thus, the microstate of the 3F term is 21

The correct answer is 3s₁ .

Concept: -

The three rules are:

1. For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to 2s +1, where (s) is the total spin angular momentum for all electrons. The multiplicity is also equal to the number of unpaired electrons plus one. Therefore, the term with lowest energy is also the term with maximum s and maximum number of unpaired electrons with equal spin angular momentum (either +1/2 or -1/2).
2. For a given multiplicity, the term with the largest value of the total orbital angular momentum quantum number L has the lowest energy.
3. For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number J , J =L+S lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of J is lowest in energy.

Explanation: -

1s¹ 2s¹ 

s = \(\frac 1 2\)x 2= 1

S.M (spin multiplicity S) = 2s +1

                                   = 2 x 1 + 1

                                   = 3

J = L +S 

   = 0 + 1 = 1 

Lowest energy state is ³S₁.

Conclusion: -

The lowest energy electronic state is 3S1.

The correct answer is \(\rm ^3\Sigma_g^-\)

Concept:-

The term symbol for the ground state of a diatomic molecule like B₂ (boron) can be determined based on its electronic configuration. 

Boron has five electrons, and when forming a diatomic molecule like (B2), we need to consider the molecular orbital diagram. The molecular orbital diagram for (B2) can be constructed using molecular orbital theory.

Explanation:-

For the ground state of (B2), the molecular orbital diagram typically involves filling the sigma and pi molecular orbitals with electrons. The ground state electronic configuration can be represented as \(\sigma_g^2 \sigma_u^2 \pi_u^2 \)

Now, let's determine the term symbol. The term symbol is given by:

\( ^{2S+1} \Lambda_{\Sigma} \)

where:
S is the total spin quantum number,
(\((\Lambda)\) is the projection of the electronic angular momentum along the internuclear axis, and
\((\Sigma)\) is the electronic spin multiplicity.

For (B2), with two unpaired electrons, the total spin quantum number (S) is (1), and the electronic spin multiplicity \((\Sigma)\) is (2S + 1 = 3). The projection of the electronic angular momentum along the internuclear axis \((\Lambda)\) for a sigma bond is (0).

Conclusion:-

So, the term symbol for the ground state of  is (B2) is \((^3\Sigma_g)\).

The correct answer is F

Concept:-

• Quantum Numbers: These are a set of values which gives complete information about the probability location and energy of an electron in an atom. They define the size, shape, and orientation in space of an individual electron's orbit.
• Pauli Exclusion Principle: This principle states that no two electrons in an atom can share the same set of four quantum numbers. This means that any given orbital can hold a maximum of two electrons and those electrons must have opposite spins.
• Hund's Rules: Hund's rules state that the most stable electron configuration is the one with the maximum values for the total spin quantum number and the total orbital quantum number.
• Electron Configuration: Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of F (Fluorine) in its ground state is [He]2s²2p⁵.
• Term Symbols: Term symbols are used to represent different energy levels in an atom. The general notation for a term symbol is 2S+1LJ where S is the total spin quantum number, L is the total orbital quantum number, and J is the total angular momentum quantum number.
• Ground State: The ground state of an atom is the state of the atom with the lowest possible energy where all electrons occupy the lowest possible orbitals.

Explanation:-

• The atom represented by the term ²P_3/2 is F (Fluorine).
• Fluorine has an electron configuration of [He]2s^22p^5. The 2p orbitals are partially filled here. In the p orbitals, the total number of unpaired electrons spin is 1, which gives a total spin S=1/2.
• The electrons in the 2p orbitals give a total orbital quantum number L=1, since every p orbital has an L value of 1. In calculating the total orbital quantum number, the sum of all individual orbital quantum numbers is taken, which gives L=1.
• According to Hund's rule, electrons strive to occupy their own orbitals before paring up, for example, fluorine has one unpaired electron.
• For less than half-filled shells, J should be lowest and is equal to |L-S|. Here J=1/2.
• The term symbol is given by 2S+1L_J. Using the quantum numbers obtained, the term symbol for fluorine in its ground state is 2P_3/2.

Wrong Answer Reasoning:

• H (Wrong): Hydrogen only has one electron and resides in the 1s orbital. The term symbol for this element should be 2S_1/2, not 2P_3/2.
• B (Wrong): Boron has an electron configuration of [He]2s²2p¹. With only one electron in the 2p orbital, Boron would have a term symbol of 2P_1/2, not the given 2P_3/2.
• Li (Wrong): Lithium has an electron configuration of [He]2s¹. There are no p orbital electrons in Lithium, so the term symbol can't be 2P_3/2. The term symbol for Lithium is 2S_1/2.

Conclustion:-

So, 2P3/2 is the ground state of F