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Lanthanoids and Actinoids Questions in English

Class 12 Chemistry · d-and f-Block Elements · Lanthanoids and Actinoids

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101
DifficultMCQ
$Ln$ (Lanthanide) $\xrightarrow{\text{With Halogen}} X$
$Ln$ (Lanthanide) $\xrightarrow{\text{Burn With } O_2} Y$
$Ln$ (Lanthanide) $\xrightarrow{\text{Heated with } N_2} Z$
$X, Y$ and $Z$ are respectively:-
A
$LnX_3, Ln_2O_3, Ln_3N$
B
$LnX_3, Ln_2O_3, LnN$
C
$LnX_2, LnO, LnN$
D
$LnX_2, Ln_2O_3, Ln_3N$

Solution

(B) Lanthanides $(Ln)$ react with halogens $(X_2)$ to form trihalides $(LnX_3)$.
When burned in oxygen $(O_2)$,they form sesquioxides $(Ln_2O_3)$.
When heated with nitrogen $(N_2)$,they form nitrides $(LnN)$.
Therefore,$X = LnX_3$,$Y = Ln_2O_3$,and $Z = LnN$.
102
EasyMCQ
The Lanthanoid contraction is responsible for the fact that
A
$Zr$ and $Y$ have about same radius
B
$Zr$ and $Nb$ have similar oxidation state
C
$Zr$ and $Hf$ have about the same radius
D
$Zr$ and $Zn$ have the same oxidation state

Solution

(C) The elements following the lanthanoids in the periodic table are influenced by the lanthanoid contraction.
For example, the atomic radius of the metal zirconium, $Zr$, (a period $-5$ transition element) is $159 \ pm$ and that of hafnium, $Hf$, (the corresponding period $-6$ element) is $156 \ pm$.
The radii are very similar even though the number of electrons increases from $40$ to $72$ and the atomic mass increases from $91.22$ to $178.49 \ g/mol$.
The increase in mass and the nearly unchanged radii lead to a steep increase in density from $6.51$ to $13.35 \ g/cm^3$.
Zirconium and hafnium, therefore, have very similar chemical behaviour, having closely similar radii and electron configurations.
Radius-dependent properties such as lattice energies, solvation energies, and stability constants of complexes are also similar.
103
MediumMCQ
Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids,the main reason being
A
Lesser energy difference between $5f$ and $6d$ than $4f$ and $5d$ orbitals
B
More energy difference between $5f$ and $6d$ than between $4f$ and $5d$ orbitals
C
Less reactive nature of the actinoids than the lanthanoids
D
$4f$ orbitals are more diffused than $5f$ orbitals

Solution

(A) The $5f$,$6d$,and $7s$ energy levels in actinoids are of comparable energy.
Because of this small energy gap,electrons from all these orbitals can participate in bonding,leading to a larger number of oxidation states.
In contrast,in lanthanoids,the $4f$ orbitals are deeply buried and have a much larger energy difference compared to $5d$ orbitals,restricting the number of oxidation states.
104
EasyMCQ
The correct order of ionic radii of $Ce$,$La$,$Pm$ and $Yb$ in $+3$ oxidation state is
A
$La^{+3} < Pm^{+3} < Ce^{+3} < Yb^{+3}$
B
$La^{+3} < Ce^{+3} < Pm^{+3} < Yb^{+3}$
C
$Yb^{+3} < Ce^{+3} < Pm^{+3} < La^{+3}$
D
$Yb^{+3} < Pm^{+3} < Ce^{+3} < La^{+3}$

Solution

(D) In the lanthanoid series,as we move from $La$ $(Z=57)$ to $Lu$ $(Z=71)$,the ionic radii of the $+3$ ions decrease regularly. This phenomenon is known as lanthanoid contraction.
This decrease occurs because the $4f$ electrons are added,which provide poor shielding for the increasing nuclear charge,leading to a stronger attraction between the nucleus and the outer electrons.
The atomic numbers are: $La$ $(57)$,$Ce$ $(58)$,$Pm$ $(61)$,and $Yb$ $(70)$.
Therefore,the order of ionic radii is $La^{+3} > Ce^{+3} > Pm^{+3} > Yb^{+3}$,which is equivalent to $Yb^{+3} < Pm^{+3} < Ce^{+3} < La^{+3}$.
105
EasyMCQ
In the lanthanide series,the basicity of the lanthanide hydroxides:
A
Increases
B
Decreases
C
First increases then decreases
D
First decreases then increases

Solution

(B) Across the lanthanide series,the ionic radius of the $Ln^{3+}$ ions decreases due to lanthanide contraction.
As the size of the $Ln^{3+}$ cation decreases,the $Ln-OH$ bond becomes more covalent and less ionic.
Since basicity is directly related to the ease of releasing $OH^-$ ions,the decrease in ionic character leads to a decrease in basicity.
Therefore,the basicity of lanthanide hydroxides decreases from $La(OH)_3$ to $Lu(OH)_3$.
106
EasyMCQ
Which is not the correct statement? (At. nos. $Ce = 58, Lu = 71, La = 57, Yb = 70$)
A
Colour of $Yb^{3+}$ ion is pink.
B
$La^{3+}$ is diamagnetic.
C
$Ce^{4+}$ has $f^0$ configuration.
D
$Lu^{3+}$ has $f^{14}$ configuration.

Solution

(A) The electronic configuration of $Yb$ $(Z=70)$ is $[Xe] 4f^{14} 6s^2$.
Thus,$Yb^{3+}$ has the configuration $[Xe] 4f^{13}$.
Since it has an unpaired electron,it should be paramagnetic,but $Yb^{3+}$ ions are colorless in aqueous solution because the $f-f$ transitions are not observed in the visible region.
Therefore,the statement that $Yb^{3+}$ is pink is incorrect.
107
MediumMCQ
Which of the following forms a stable $+4$ oxidation state?
A
$La$ $(Z = 57)$
B
$Eu$ $(Z = 63)$
C
$Ce$ $(Z = 58)$
D
$Gd$ $(Z = 64)$

Solution

(C) The electronic configuration of $Ce$ $(Z = 58)$ is $[Xe] 4f^1 5d^1 6s^2$.
By losing four electrons,it attains the stable noble gas configuration of $Xe$ $([Xe])$,making the $+4$ oxidation state stable for $Ce$.
108
EasyMCQ
What is the effect of lanthanoid contraction in the lanthanoid series of elements?
A
Increase in both atomic and ionic radii
B
Decrease in atomic radii and increase in ionic radii
C
Decrease in both atomic and ionic radii
D
Increase in atomic radii and decrease in ionic radii

Solution

(C) Lanthanoid contraction refers to the steady decrease in the atomic and ionic radii of the lanthanoid elements as the atomic number increases from $La$ $(Z=57)$ to $Lu$ $(Z=71)$.
This occurs due to the poor shielding effect of the $4f$ electrons,which causes the effective nuclear charge to increase,pulling the valence shell closer to the nucleus.
109
MediumMCQ
The correct order of atomic radii is
A
$Eu > Ce > Nd > Ho$
B
$Ho > Nd > Eu > Ce$
C
$Ce > Eu > Ho > Nd$
D
$Eu > Nd > Ce > Ho$

Solution

(A) The atomic radii of the given lanthanoids are as follows:
$Eu = 199 \text{ pm}$
$Ce = 183 \text{ pm}$
$Nd = 181 \text{ pm}$
$Ho = 176 \text{ pm}$
Therefore, the correct order of atomic radii is $Eu > Ce > Nd > Ho$.
110
EasyMCQ
The lanthanoid that would show color is
A
$Gd^{3+}$
B
$La^{3+}$
C
$Lu^{3+}$
D
$Sm^{3+}$

Solution

(D) The color of lanthanoid ions depends on the presence of unpaired $f$-electrons.
$La^{3+}$ has a configuration of $[Xe] 4f^0$ (no unpaired electrons).
$Gd^{3+}$ has a configuration of $[Xe] 4f^7$ (half-filled,stable,but colorless in many compounds due to high energy transition).
$Lu^{3+}$ has a configuration of $[Xe] 4f^{14}$ (fully filled,no unpaired electrons).
$Sm^{3+}$ has a configuration of $[Xe] 4f^5$,which contains unpaired electrons,allowing for $f-f$ transitions that result in a yellow color.
111
MediumMCQ
The maximum number of possible oxidation states of actinoids are shown by
A
berkelium $(Bk)$ and californium $(Cf)$
B
nobelium $(No)$ and lawrencium $(Lr)$
C
actinium $(Ac)$ and thorium $(Th)$
D
neptunium $(Np)$ and plutonium $(Pu)$

Solution

(D) The actinoids exhibit a range of oxidation states due to the comparable energies of the $5f$,$6d$,and $7s$ orbitals.
Neptunium $(Np)$ and plutonium $(Pu)$ exhibit the maximum number of oxidation states among the actinoids,reaching up to $+7$.
This wide range is possible because the energy levels of the $5f$,$6d$,and $7s$ orbitals are very close,allowing a larger number of electrons to participate in bond formation.
112
DifficultMCQ
The highest possible oxidation states of uranium and plutonium,respectively,are
A
$6$ and $4$
B
$7$ and $6$
C
$4$ and $6$
D
$6$ and $7$

Solution

(D) The electronic configuration of $U$ $(Z=92)$ is $[Rn] 5f^3 6d^1 7s^2$. The highest oxidation state shown by $U$ is $+6$.
The electronic configuration of $Pu$ $(Z=94)$ is $[Rn] 5f^6 7s^2$. The highest oxidation state shown by $Pu$ is $+7$.
113
EasyMCQ
An element with electronic configuration $[Rn]\, 7s^2\, 5f^3\, 6d^1$ will fall in
A
Period no. $= 6$,group no. $= 5$,Block $= d$
B
Period no. $= 7$,group no. $= III\, B$,Block $= f$
C
Period no. $= 7$,group no. $= 5$,Block $= d$
D
Period no. $= 6$,group no. $= III\, B$,Block $= f$

Solution

(B) The given electronic configuration is $[Rn]\, 7s^2\, 5f^3\, 6d^1$.
$1$. The highest principal quantum number $(n)$ is $7$,which indicates that the element belongs to Period $7$.
$2$. The last electron enters the $5f$ orbital,which classifies the element as an $f$-block element (Actinoid series).
$3$. All $f$-block elements belong to Group $3$ (or $III\, B$ in the older $IUPAC$ notation).
Therefore,the element belongs to Period $7$,Group $3$ $(III\, B)$,and $f$-block.
114
EasyMCQ
Find the atomic number of the element at which pairing in the $4f$ orbital starts.
A
$57$
B
$58$
C
$64$
D
$65$

Solution

(D) The electronic configuration of Lanthanum $(Z=57)$ is $[Xe] 5d^1 6s^2$.
The filling of the $4f$ orbital begins with Cerium $(Z=58)$,which has the configuration $[Xe] 4f^1 5d^1 6s^2$.
As we proceed through the Lanthanide series,electrons are added to the $4f$ subshell.
Pairing in the $4f$ orbital starts when the $8^{th}$ electron enters the $4f$ subshell,which corresponds to Gadolinium $(Z=64)$.
The configuration of Gadolinium is $[Xe] 4f^7 5d^1 6s^2$,and the next element,Terbium $(Z=65)$,has the configuration $[Xe] 4f^9 6s^2$ (or $[Xe] 4f^8 5d^1 6s^2$),where the $8^{th}$ electron forces pairing in the $4f$ orbital.
115
MediumMCQ
Most acidic among the given compounds is:
A
$Pr(OH)_3$
B
$Gd(OH)_3$
C
$Sm(OH)_3$
D
$Er(OH)_3$

Solution

(D) The basicity of lanthanoid hydroxides $Ln(OH)_3$ decreases as the ionic radius of the $Ln^{3+}$ ion decreases due to lanthanoid contraction.
As we move from $Pr$ to $Er$ in the lanthanoid series,the ionic radius decreases $(Pr^{3+} > Sm^{3+} > Gd^{3+} > Er^{3+})$.
Therefore,the basicity order is $Pr(OH)_3 > Sm(OH)_3 > Gd(OH)_3 > Er(OH)_3$.
Since acidity is inversely proportional to basicity,the most acidic compound is the one with the smallest ionic radius,which is $Er(OH)_3$.
116
MediumMCQ
Which statement is incorrect for the electronic configuration $[Xe]\, 4f^{7}\, 5d^{1}\, 6s^{2}$?
A
It is placed in the $d-$block,$IIIB$ group,$6^{th}$ period.
B
It is a natural element.
C
It has the maximum number of unpaired $e^{-}$ in the lanthanoid series.
D
It is $Gd$.

Solution

(A) The electronic configuration $[Xe]\, 4f^{7}\, 5d^{1}\, 6s^{2}$ corresponds to Gadolinium ($Gd$,atomic number $64$).
$Gd$ belongs to the lanthanoid series,which are $f-$block elements,not $d-$block elements.
Therefore,the statement that it is placed in the $d-$block is incorrect.
$Gd$ has $7$ unpaired electrons in the $4f$ orbital and $1$ in the $5d$ orbital,totaling $8$ unpaired electrons,which is the maximum for lanthanoids.
It is a naturally occurring element.
117
MediumMCQ
The correct order of ionic radii of $Ce, La, Pm$ and $Yb$ in $+3$ oxidation state is:
A
$La^{3+} < Pm^{3+} < Ce^{3+} < Yb^{3+}$
B
$La^{3+} < Ce^{3+} < Pm^{3+} < Yb^{3+}$
C
$Yb^{3+} < Ce^{3+} < Pm^{3+} < La^{3+}$
D
$Yb^{3+} < Pm^{3+} < Ce^{3+} < La^{3+}$

Solution

(D) Due to lanthanoid contraction,the ionic radii of $f$-block elements decrease from $La$ to $Lu$ as the atomic number increases.
Since the atomic numbers are $La (57)$,$Ce (58)$,$Pm (61)$,and $Yb (70)$,the ionic radii follow the order: $La^{3+} > Ce^{3+} > Pm^{3+} > Yb^{3+}$.
Therefore,the correct order is $Yb^{3+} < Pm^{3+} < Ce^{3+} < La^{3+}$.
118
MediumMCQ
If the atomic number of an element is $58,$ it will be placed in the periodic table in the
A
$III-B$ group and $6^{th}$ period
B
$IV-B$ group and $6^{th}$ period
C
$V-B$ group and $7^{th}$ period
D
none of these

Solution

(A) The electronic configuration of the element with atomic number $58$ (Cerium,$Ce$) is $[Xe] \ 4f^1 \ 5d^1 \ 6s^2$.
Since the last electron enters the $4f$ orbital,it is a lanthanoid element.
All lanthanoids belong to group $III-B$ (or group $3$) and the $6^{th}$ period of the periodic table.
119
EasyMCQ
Which statement is incorrect among the following?
A
Lanthanoid hydroxides are less basic in nature as compared to actinoid hydroxides.
B
Lanthanoids form oxocations.
C
In lanthanoids,only promethium is radioactive.
D
Actinoids form oxocations.

Solution

(B) $1$. Lanthanoid hydroxides are less basic than actinoid hydroxides due to the higher ionic character of actinoid-oxygen bonds. This statement is correct.
$2$. Lanthanoids generally do not form oxocations (like $UO_2^{2+}$ or $PuO_2^{2+}$),whereas actinoids are well-known for forming stable oxocations. Therefore,the statement that lanthanoids form oxocations is incorrect.
$3$. Among the lanthanoids,only promethium $(Pm)$ is radioactive. This statement is correct.
$4$. Actinoids are known to form oxocations such as $UO_2^{2+}$ and $PuO_2^{2+}$. This statement is correct.
120
DifficultMCQ
The outer electronic structure of lawrencium (atomic number $103$) is
A
$Rn\, 5f^{13} \,7s^2 \,7p^2$
B
$Rn\, 5f^{13} \,6d^1 \,7s^1 \,7p^2$
C
$Rn\, 5f^{14} \,7s^1 \,7p^2$
D
$Rn\, 5f^{14} \,6d^1 \,7s^2$

Solution

(D) Lawrencium $(Z = 103)$ is the last element of the Actinide series.
The electronic configuration of Lawrencium is $[Rn] \, 5f^{14} \, 6d^1 \, 7s^2$.
Although it was historically debated,experimental and theoretical studies confirm that the $6d$ orbital is occupied in the ground state configuration.
121
MediumMCQ
Which of the following is not a consequence of the Lanthanoid contraction?
A
$5d$ series elements have a higher $IE_1$ than $3d$ or $4d$ series
B
$Zr$ and $Hf$ have a comparable size
C
$Zr$ and $Hf$ occur together in the earth's crust in their minerals
D
High density of the sixth period elements

Solution

(A) The Lanthanoid contraction is the steady decrease in the atomic and ionic radii of the lanthanoids with increasing atomic number.
$1$. The similarity in size between $Zr$ ($4d$ series) and $Hf$ ($5d$ series) is a direct consequence of the Lanthanoid contraction.
$2$. Because $Zr$ and $Hf$ have similar sizes and chemical properties,they occur together in nature.
$3$. The high density of the sixth period elements is also a result of the Lanthanoid contraction,as the volume of the atoms decreases while the mass increases.
$4$. The $IE_1$ (first ionization energy) of $5d$ series elements is generally higher than that of $3d$ and $4d$ series elements,but this is primarily due to the poor shielding effect of $4f$ electrons and the increased effective nuclear charge,not a direct consequence of the contraction itself in the context of the other options provided.
122
EasyMCQ
Which of the following elements belongs to the actinoid series?
A
$Y$
B
$Ta$
C
$U$
D
$Pm$

Solution

(C) The actinoid series consists of elements with atomic numbers $89$ to $103$.
$U$ (Uranium,$Z=92$) belongs to the actinoid series.
$Y$ (Yttrium,$Z=39$) is a $d-$block element.
$Ta$ (Tantalum,$Z=73$) is a $d-$block element.
$Pm$ (Promethium,$Z=61$) belongs to the lanthanoid series.
123
MediumMCQ
Which transuranic elements are naturally present in trace amounts in uranium ore $U_3O_8$?
A
$Np, Pu$
B
$Np, Po$
C
$Am, Bk$
D
$Lr, Md$

Solution

(A) Transuranic elements are those with atomic numbers greater than $92$.
In uranium ores like $U_3O_8$,trace amounts of $Neptunium$ ($Np$,$Z=93$) and $Plutonium$ ($Pu$,$Z=94$) are found due to the neutron capture by $U^{238}$ followed by $\beta$-decay processes.
Therefore,the correct pair is $Np$ and $Pu$.
124
EasyMCQ
Which one of the following elements shows the maximum number of different oxidation states in its compounds?
A
$Eu$
B
$La$
C
$Gd$
D
$Am$

Solution

(D) The element $Am$ (Americium) is an actinoid. Actinoids exhibit a greater range of oxidation states compared to lanthanoids due to the comparable energies of $5f$,$6d$,and $7s$ orbitals.
$Am$ shows $+2, +3, +4, +5, +6,$ and $+7$ oxidation states,which is the maximum among the given options.
125
MediumMCQ
For the general electronic configuration $(n-2)f^{1-14}(n-1)d^{0-1}ns^2$,if $n=7$,the configuration belongs to which series?
A
Lanthanides
B
Actinides
C
Transition elements
D
None of these

Solution

(B) The general electronic configuration $(n-2)f^{1-14}(n-1)d^{0-1}ns^2$ represents the $f$-block elements.
For $n=6$,the configuration is $4f^{1-14}5d^{0-1}6s^2$,which corresponds to the Lanthanides.
For $n=7$,the configuration is $5f^{1-14}6d^{0-1}7s^2$,which corresponds to the Actinides.
126
MediumMCQ
Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids,the main reason being
A
Lesser energy difference between $5f$ and $6d$ than $4f$ and $5d$ orbitals
B
More energy difference between $5f$ and $6d$ than between $4f$ and $5d$ orbitals
C
More reactive nature of the actinoids than the lanthanoids
D
$4f$ orbitals are more diffused than $5f$ orbitals

Solution

(A) The energy difference between $5f$ and $6d$ orbitals is smaller than the energy difference between $4f$ and $5d$ orbitals.
Because of this smaller energy gap,the electrons in actinoids can be removed from both $5f$ and $6d$ orbitals.
Consequently,actinoids exhibit a greater variety of oxidation states compared to lanthanoids.
127
EasyMCQ
$A$ lanthanoid has $n$ unpaired electrons and another lanthanoid has $(14-n)$ unpaired electrons. It means:
A
Both lanthanoids show the same colour
B
Both show the same magnetic behaviour
C
Both $(A)$ and $(B)$
D
Both are radioactive

Solution

(C) The number of unpaired electrons in a lanthanoid ion is determined by the $4f$ orbital configuration.
For a lanthanoid with $n$ unpaired electrons,the electronic configuration of the $4f$ subshell is $f^n$.
For a lanthanoid with $(14-n)$ unpaired electrons,the electronic configuration is $f^{14-n}$.
According to the principle of electronic configuration in $f$-orbitals,an $f^n$ configuration and an $f^{14-n}$ configuration have the same number of unpaired electrons.
For example,$f^1$ and $f^{13}$ both have $1$ unpaired electron,and $f^2$ and $f^{12}$ both have $2$ unpaired electrons.
Since both have the same number of unpaired electrons,they exhibit the same magnetic behaviour (paramagnetism) and the same colour due to $f-f$ transitions.
128
MediumMCQ
Which of the following compounds is the most acidic?
A
$Pr(OH)_3$
B
$Gd(OH)_3$
C
$Sm(OH)_3$
D
$Er(OH)_3$

Solution

(D) In the lanthanoid series,the ionic radius decreases from left to right due to lanthanoid contraction.
As the ionic radius decreases,the covalent character of the $M-OH$ bond increases,which leads to an increase in the acidic nature of the hydroxides.
Therefore,the acidity increases as we move from $Pr$ to $Er$ in the periodic table.
Among the given options,$Er(OH)_3$ is the most acidic.
129
EasyMCQ
The electronic configuration of Curium (Atomic number $96$) is
A
$[Rn]\, 5f^3\, 6d^5\, 7s^2$
B
$[Rn]\, 5f^7\, 6d^2\, 7s^1$
C
$[Rn]\, 5f^7\, 6d^1\, 7s^2$
D
$[Rn]\, 5f^8\, 6d^6\, 7s^2$

Solution

(C) The atomic number of Curium $(Cm)$ is $96$.
Its electronic configuration is based on the Radon $(Rn)$ core,which is $[Rn] = [Xe]\, 4f^{14}\, 5d^{10}\, 6s^2\, 6p^6$.
The $5f$ subshell is filled after the $6d$ and $7s$ orbitals.
For Curium $(Z=96)$,the configuration is $[Rn]\, 5f^7\, 6d^1\, 7s^2$.
130
EasyMCQ
The electronic configuration of $Yb^{2+}$ is:
A
$[Xe] \, 4f^{14} \, 5d^1$
B
$[Xe] \, 4f^{14}$
C
$[Xe] \, 4f^{14} \, 6s^2$
D
$[Xe] \, 4f^{14} \, 5d^1 \, 6s^2$

Solution

(B) The atomic number of $Yb$ (Ytterbium) is $70$.
The ground state electronic configuration of $Yb$ is $[Xe] \, 4f^{14} \, 6s^2$.
When $Yb$ forms the $Yb^{2+}$ ion,it loses two electrons from the outermost $6s$ orbital.
Therefore,the electronic configuration of $Yb^{2+}$ is $[Xe] \, 4f^{14}$.
131
MediumMCQ
Which one of the following statements concerning lanthanide elements is false?
A
Lanthanides are separated from one another by ion exchange method.
B
The ionic radii of trivalent lanthanides steadily increase with increase in atomic number.
C
All lanthanides are highly dense metals.
D
Most characteristic oxidation state of lanthanides is $+3$.

Solution

(B) The ionic radii of trivalent lanthanides decrease progressively with an increase in atomic number. This phenomenon is known as lanthanide contraction. Therefore,the statement that ionic radii increase with atomic number is false.
132
MediumMCQ
Consider the following statements:
$I$. $La(OH)_3$ is the least basic among hydroxides of lanthanides.
$II$. $Zr^{4+}$ and $Hf^{4+}$ possess almost the same ionic radii.
$III$. $Ce^{4+}$ can act as an oxidizing agent.
Which of the above is/are true?
A
$I$ and $III$
B
$II$ and $III$
C
$II$ only
D
$I$ and $II$

Solution

(B) $I$. $La(OH)_3$ is the most basic among lanthanide hydroxides because basicity decreases as the ionic radius decreases from $La$ to $Lu$. Thus,statement $I$ is false.
$II$. Due to lanthanide contraction,the ionic radii of $Zr^{4+}$ $(0.79 \ \mathring{A})$ and $Hf^{4+}$ $(0.78 \ \mathring{A})$ are almost identical. Thus,statement $II$ is true.
$III$. $Ce^{4+}$ is a strong oxidizing agent because it readily gains an electron to attain the more stable $Ce^{3+}$ oxidation state. Thus,statement $III$ is true.
Therefore,statements $II$ and $III$ are true.
133
AdvancedMCQ
Assertion : Magnetic moment of $Dy^{3+}$ is highest among lanthanoids.
Reason : Orbital motion contributes to the magnetic moment.
A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

Solution

(A) In lanthanide ions,the $4f$ electrons are well-shielded from the external field by the overlying $5s$ and $5p$ electrons. Thus,the magnetic effect of the orbital motion of the electron is not quenched. Consequently,the magnetic moment must be calculated by taking into account both the spin and orbital contributions.
The magnetic moment is given by $\mu = g\sqrt{J(J+1)}$,where $g = 1 + \frac{S(S+1) - L(L+1) + J(J+1)}{2J(J+1)}$.
For $Dy^{3+}$ $([Xe]4f^9)$,the $4f$ subshell is more than half-filled. In such cases,the spin and orbital angular momenta couple to give a high total angular momentum $J$,resulting in the highest magnetic moment among lanthanoids.
Therefore,both the Assertion and Reason are correct,and the Reason is the correct explanation of the Assertion.
134
MediumMCQ
Assertion : Europium $(II)$ is more stable than cerium $(II)$.
Reason : Cerium salts are used as catalyst in petroleum cracking.
A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

Solution

(C) The electronic configuration of $Eu^{2+}$ is $[Xe] 4f^7$,which is a half-filled $f$-orbital configuration,providing extra stability.
The electronic configuration of $Ce^{2+}$ is $[Xe] 4f^1 5d^1$,which is less stable.
Therefore,the Assertion is correct.
Cerium salts are generally not used as catalysts in petroleum cracking; rather,zeolites or other specific catalysts are used. Thus,the Reason is incorrect.
135
MediumMCQ
Assertion : Magnetic moment values of actinides are lesser than the theoretically predicted values.
Reason : Actinide elements are strongly paramagnetic.
A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

Solution

(B) The magnetic moment values of actinides are lower than the theoretically predicted values because the $5f$ electrons are less effectively shielded by the outer shells. This leads to the quenching of the orbital contribution to the magnetic moment,making the observed values smaller than those calculated using the spin-only formula. While actinides are paramagnetic,the reason provided does not explain why the magnetic moments are lower than predicted.
136
MediumMCQ
The electronic configurations of bivalent europium and trivalent cerium are
(atomic number : $Xe=54, Ce=58, Eu=63$ )
A
$[Xe] 4f^{4}$ and $[Xe] 4f^{9}$
B
$[Xe] 4f^{7}$ and $[Xe] 4f^{1}$
C
$[Xe] 4f^{7} 6s^{2}$ and $[Xe] 4f^{2} 6s^{2}$
D
$[Xe] 4f^{2}$ and $[Xe] 4f^{7}$

Solution

(B) The atomic number of $Eu$ is $63$. The electronic configuration of $Eu$ is $[Xe] 4f^{7} 6s^{2}$.
For $Eu^{2+}$,two electrons are removed from the $6s$ orbital,resulting in $[Xe] 4f^{7}$.
The atomic number of $Ce$ is $58$. The electronic configuration of $Ce$ is $[Xe] 4f^{1} 5d^{1} 6s^{2}$.
For $Ce^{3+}$,three electrons are removed (two from $6s$ and one from $5d$),resulting in $[Xe] 4f^{1}$.
137
EasyMCQ
Name a member of the lanthanoid series which is well known to exhibit $+4$ oxidation state.
A
Cerium
B
Lanthanum
C
Gadolinium
D
Promethium

Solution

(A) The lanthanoid series elements typically exhibit a $+3$ oxidation state. However,Cerium $(Z=58)$ is well known to exhibit a $+4$ oxidation state because it achieves a stable noble gas configuration $([Xe]4f^0)$ upon losing four electrons.
138
Medium
Actinoid contraction is greater from element to element than lanthanoid contraction. Why?

Solution

(N/A) In actinoids,$5f$ orbitals are filled. These $5f$ orbitals have a poorer shielding effect than $4f$ orbitals (in lanthanoids).
Thus,the effective nuclear charge experienced by electrons in valence shells in the case of actinoids is much greater than that experienced by lanthanoids.
Hence,the size contraction in actinoids is greater as compared to that in lanthanoids.
139
Medium
What is lanthanoid contraction? What are the consequences of lanthanoid contraction?

Solution

(N/A) As we move along the lanthanoid series,the atomic number increases gradually by $1$. This means that the number of electrons and protons present in an atom also increases by $1$. As electrons are being added to the same shell,the effective nuclear charge increases. This happens because the increase in nuclear attraction due to the addition of a proton is more pronounced than the increase in the interelectronic repulsions due to the addition of an electron. Also,with the increase in atomic number,the number of electrons in the $4f$ orbital also increases. The $4f$ electrons have poor shielding effect. Therefore,the effective nuclear charge experienced by the outer electrons increases. Consequently,the attraction of the nucleus for the outermost electrons increases. This results in a steady decrease in the size of lanthanoids with the increase in the atomic number. This is termed as lanthanoid contraction.
Consequences of lanthanoid contraction:
$i$. There is similarity in the properties of the second and third transition series.
$ii$. Separation of lanthanoids is possible due to lanthanoid contraction.
$iii$. It is due to lanthanoid contraction that there is a variation in the basic strength of lanthanoid hydroxides. (Basic strength decreases from $La(OH)_3$ to $Lu(OH)_3$).
140
Medium
What are the different oxidation states exhibited by the lanthanoids?

Solution

(N/A) In the lanthanoid series,the $+3$ oxidation state is the most common,meaning $Ln(III)$ compounds are predominant. However,$+2$ and $+4$ oxidation states are also observed in certain solutions or solid compounds.
141
Difficult
Compare the chemistry of actinoids with that of the lanthanoids with special reference to:
$(i)$ electronic configuration
$(ii)$ atomic and ionic sizes
$(iii)$ oxidation state
$(iv)$ chemical reactivity.

Solution

(N/A) $(i)$ Electronic configuration: The general electronic configuration for lanthanoids is $[Xe] \ 4f^{0-14} \ 5d^{0-1} \ 6s^2$ and that for actinoids is $[Rn] \ 5f^{1-14} \ 6d^{0-1} \ 7s^2$. Unlike $4f$ orbitals,$5f$ orbitals are not deeply buried and participate in bonding to a greater extent.
$(ii)$ Atomic and ionic sizes: Similar to lanthanoid contraction,actinoids exhibit actinoid contraction (overall decrease in atomic and ionic radii). The contraction is greater in actinoids due to the poorer shielding effect of $5f$ orbitals compared to $4f$ orbitals.
$(iii)$ Oxidation states: The principal oxidation state of lanthanoids is $+3$. However,$+2$ and $+4$ states are also observed due to the stability of empty,half-filled,or fully-filled $f$-orbitals. Actinoids exhibit a greater range of oxidation states (e.g.,$+3, +4, +5, +6, +7$) because the $5f, 6d,$ and $7s$ energy levels are of comparable energies.
$(iv)$ Chemical reactivity: Lanthanoids are highly reactive,similar to calcium,but reactivity decreases with increasing atomic number. Actinoids are highly reactive metals,especially when finely divided. They react with boiling water to form oxides and hydrides and combine with most non-metals at moderate temperatures. They are generally unaffected by alkalies,and their reaction with nitric acid is limited due to the formation of a protective oxide layer.
142
Easy
What are alloys? Name an important alloy which contains some of the lanthanoid metals. Mention its uses.

Solution

(N/A) An alloy is a solid solution of two or more elements in a metallic matrix. It can either be a partial solid solution or a complete solid solution. Alloys usually possess different physical properties than those of the component elements.
An important alloy of lanthanoids is Mischmetal. It contains lanthanoids $(94-95 \%)$,iron $(5 \%)$,and traces of $S$,$C$,$Si$,$Ca$,and $Al$.
Uses:
$(1)$ Mischmetal is used in cigarette and gas lighters.
$(2)$ It is used in flame-throwing tanks.
$(3)$ It is used in tracer bullets and shells.
143
Easy
What are inner transition elements? Decide which of the following atomic numbers are the atomic numbers of the inner transition elements: $29, 59, 74, 95, 102, 104$.

Solution

Inner transition elements are those elements in which the last electron enters the $f$-orbital. These elements are also known as $f$-block elements,where the $4f$ and $5f$ orbitals are progressively filled.
Lanthanoids range from atomic numbers $58$ to $71$ ($4f$ series).
Actinoids range from atomic numbers $90$ to $103$ ($5f$ series).
Comparing the given atomic numbers:
$29$ is $Cu$ ($d$-block),
$59$ is $Pr$ (Lanthanoid),
$74$ is $W$ ($d$-block),
$95$ is $Am$ (Actinoid),
$102$ is $No$ (Actinoid),
$104$ is $Rf$ ($d$-block).
Therefore,the atomic numbers of the inner transition elements are $59, 95,$ and $102$.
144
Easy
The chemistry of the actinoid elements is not so smooth as that of the lanthanoids. Justify this statement by giving some examples from the oxidation states of these elements.

Solution

(N/A) Lanthanoids primarily show a stable $+3$ oxidation state. They display a limited number of oxidation states because the energy gap between $4f$,$5d$,and $6s$ orbitals is quite large.
On the other hand,the energy difference between $5f$,$6d$,and $7s$ orbitals in actinoids is very small.
Consequently,actinoids exhibit a wide range of oxidation states.
For example,uranium $(U)$ and plutonium $(Pu)$ display $+3, +4, +5,$ and $+6$ oxidation states,while neptunium $(Np)$ displays $+3, +4, +5,$ and $+7$ oxidation states.
145
Easy
Which is the last element in the series of the actinoids? Write the electronic configuration of this element. Comment on the possible oxidation state of this element.

Solution

(N/A) The last element in the actinoid series is lawrencium,$Lr$. Its atomic number is $103$ and its electronic configuration is $[Rn] \, 5f^{14} \, 6d^{1} \, 7s^{2}$. The most common oxidation state displayed by it is $+3$; because after losing $3$ electrons it attains stable $f^{14}$ configuration.
146
Easy
Use Hund's rule to derive the electronic configuration of $Ce^{3+}$ ion and calculate its magnetic moment on the basis of 'spin-only' formula.

Solution

(D) The atomic number of $Ce$ is $58$. The electronic configuration of $Ce$ is $[Xe] 4f^{1} 5d^{1} 6s^{2}$.
To form $Ce^{3+}$,three electrons are removed (two from $6s$ and one from $5d$ or $4f$ depending on the energy levels; for $Ce^{3+}$,the configuration is $[Xe] 4f^{1}$).
Thus,the electronic configuration of $Ce^{3+}$ is $[Xe] 4f^{1}$.
There is $n = 1$ unpaired electron in the $4f$ orbital.
The 'spin-only' magnetic moment formula is $\mu = \sqrt{n(n+2)} \ BM$.
Substituting $n = 1$:
$\mu = \sqrt{1(1+2)} = \sqrt{3} = 1.732 \ BM$.
147
Medium
Name the members of the lanthanoid series which exhibit $+4$ oxidation state and those which exhibit $+2$ oxidation state. Try to correlate this type of behavior with the electronic configurations of these elements.

Solution

(N/A) The lanthanoids that exhibit $+2$ and $+4$ oxidation states are listed in the table below:
$+2$ Oxidation State $+4$ Oxidation State
$Nd \ (60), Sm \ (62), Eu \ (63), Tm \ (69), Yb \ (70)$ $Ce \ (58), Pr \ (59), Nd \ (60), Tb \ (65), Dy \ (66)$

Correlation with electronic configuration:
$1$. $Ce^{4+}$ $([Xe] \ 4f^0)$ attains a stable noble gas configuration.
$2$. $Tb^{4+}$ $([Xe] \ 4f^7)$ attains a stable half-filled $f$-orbital configuration.
$3$. $Eu^{2+}$ $([Xe] \ 4f^7)$ attains a stable half-filled $f$-orbital configuration.
$4$. $Yb^{2+}$ $([Xe] \ 4f^{14})$ attains a stable fully-filled $f$-orbital configuration.
148
Medium
Compare the chemistry of the actinoids with that of lanthanoids with reference to:
$(i)$ electronic configuration
$(ii)$ oxidation states and
$(iii)$ chemical reactivity.

Solution

(A) Electronic configuration:
The general electronic configuration for lanthanoids is $[Xe]^{54} 4f^{0-14} 5d^{0-1} 6s^{2}$ and that for actinoids is $[Rn]^{86} 5f^{1-14} 6d^{0-1} 7s^{2}$. Unlike $4f$ orbitals,$5f$ orbitals are not deeply buried and participate in bonding to a greater extent.
Oxidation states:
The principal oxidation state of lanthanoids is $+3$. However,sometimes we also encounter oxidation states of $+2$ and $+4$ due to the extra stability of fully-filled and half-filled orbitals. Actinoids exhibit a greater range of oxidation states because the $5f, 6d,$ and $7s$ levels are of comparable energies. Again,$+3$ is the principal oxidation state for actinoids.
Chemical reactivity:
In the lanthanoid series,the earlier members are more reactive,with reactivity comparable to $Ca$. With an increase in atomic number,they behave similar to $Al$. Actinoids are highly reactive metals,especially when finely divided. When added to boiling water,they give a mixture of oxide and hydride. Actinoids combine with most non-metals at moderate temperatures. Alkalies have no action on them,and they are only slightly affected by nitric acid due to the formation of a protective oxide layer.
149
Medium
Write the electronic configurations of the elements with the atomic numbers $61$,$91$,$101$ and $109$.

Solution

(N/A) The electronic configurations are determined based on the Aufbau principle and the noble gas core notation:
Atomic Number Electronic Configuration
$61$ $[Xe] \, 4f^{5} \, 6s^{2}$
$91$ $[Rn] \, 5f^{2} \, 6d^{1} \, 7s^{2}$
$101$ $[Rn] \, 5f^{13} \, 7s^{2}$
$109$ $[Rn] \, 5f^{14} \, 6d^{7} \, 7s^{2}$

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