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Lanthanide contraction is due to increase in:
A.Shielding of 4f electrons
B.Atomic number
C.Effective nuclear charge
D.Size of 4f-orbital

Answer
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Hint: We know that the trend in atomic radius exhibited by Lanthanide series is described by the Lanthanide contraction. We have to know that Lanthanide contraction is applied to all the elements present in the Lanthanide series. The elements present in Lanthanide series is Cerium, Praseodymium, Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium, Ytterbium and Lutetium.

Complete step by step answer:
Lanthanide contraction is in reference to the fact of penetration of 5s and 5p orbitals to 4f subshell, so the 4f orbital is not shielded from increase in the nuclear charge that causes a decrease in atomic radius of the atom. The decrease in size is seen throughout the Lanthanides.
We know that with an increase in the number of protons, the atomic radius decreases with an increase in ionization energy. This is because of the highly positive nuclear charge and a pull on the electrons by the nucleus. The increase in effective nuclear charge leads to greater pull on the electrons. Effective nuclear charge is produced by the nucleus having more positive charge than the negative nuclear charge on the electron.
We should remember that the effect of Lanthanide contraction is due to the poor shielding of nuclear charge by electrons of 4f orbital, and therefore there is an increase in effective nuclear charge: the six-s electrons are pulled towards the nucleus, leading to decrease in atomic radius.
Lanthanide contraction is due to an increase in effective nuclear charge. Option (C) is correct.

Note:
We have to know that the poor shielding effect of the electrons present in 4f orbital causes the Lanthanide contraction. The atomic radius of the Lanthanide series decreases with an increase in atomic number. Some other factors, which contribute to Lanthanide contraction, are,
-Difficulty in the lanthanides separation
-Effect on the basic strength of hydroxides
-Formation of complex
Ionization energy of elements present in d-block.