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Which of the following pairs has the same size?
a)Fe2+ , Ni 2+
b)Zr 4+ , Ti4+ 
c)Zr 4+ , Hf 4+
d)Zn 2+ , Hf 4+
Correct answer is option 'C'. Can you explain this answer?
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Which of the following pairs has the same size?a)Fe2+ , Ni 2+b)Zr 4+ ,...
Due to lanthanide contraction, the size of Zr and Hf (atom and ions) become nearly similar
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Which of the following pairs has the same size?a)Fe2+ , Ni 2+b)Zr 4+ ,...
Explanation:


To determine which pairs have the same size, we need to consider the electronic configuration and the number of electrons in the outermost shell of the elements.

Pair a) Fe2, Ni2:
Fe2 represents the iron ion with a +2 charge, whereas Ni2 represents the nickel ion with a +2 charge.
The electronic configuration of Fe2 is 1s2 2s2 2p6 3s2 3p6 3d6, and the electronic configuration of Ni2 is 1s2 2s2 2p6 3s2 3p6 3d8.
Both Fe2 and Ni2 have the same number of electrons in the outermost d orbital, which is 8. Therefore, they have the same size.

Pair b) Zr4, Ti4:
Zr4 represents the zirconium ion with a +4 charge, whereas Ti4 represents the titanium ion with a +4 charge.
The electronic configuration of Zr4 is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d2, and the electronic configuration of Ti4 is 1s2 2s2 2p6 3s2 3p6 3d2.
The number of electrons in the outermost shell of Zr4 is 2, while the number of electrons in the outermost shell of Ti4 is 2. Therefore, they have the same size.

Pair c) Zr4, Hf4:
Zr4 represents the zirconium ion with a +4 charge, whereas Hf4 represents the hafnium ion with a +4 charge.
The electronic configuration of Zr4 is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d2, and the electronic configuration of Hf4 is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d2 5s2.
Both Zr4 and Hf4 have the same number of electrons in the outermost 4d and 5s orbitals, which is 2+2=4. Therefore, they have the same size.

Pair d) Zn2, Hf4:
Zn2 represents the zinc ion with a +2 charge, whereas Hf4 represents the hafnium ion with a +4 charge.
The electronic configuration of Zn2 is 1s2 2s2 2p6 3s2 3p6 3d10, and the electronic configuration of Hf4 is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d2 5s2.
The number of electrons in the outermost shell of Zn2 is 10, while the number of electrons in the outermost shell of Hf4 is 4+2=6. Therefore,
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