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Correct Answer: all of the above are correct
the question deals with the comparison of bond lengths between diatomic molecules of halogens, specifically cl2, br2, and i2. to understand why the bond lengths vary, we need to consider the atomic size of the halogens involved.
the atomic radius of an element is a measure of the size of its atoms, usually the mean or typical distance from the nucleus to the boundary of the surrounding cloud of electrons. atomic size increases as you move down a group in the periodic table because each successive element has an additional electron shell. thus, iodine (i), being lower in the periodic table than bromine (br) and chlorine (cl), has a larger atomic radius than bromine, which in turn has a larger atomic radius than chlorine.
the bond length between two atoms in a molecule is approximately equal to the sum of their atomic radii. when two iodine atoms form a diatomic molecule (i2), the bond length is the sum of the radii of two iodine atoms, which is quite large due to the large size of the iodine atoms. similarly, the bond length of br2 involves the sum of the radii of two bromine atoms and is shorter than that of i2 because bromine atoms are smaller than iodine atoms. the shortest of the three, cl2, involves the smallest atoms, chlorine.
therefore, the bond length increases in the order cl2 < br2 < i2, reflecting the increasing size of the atomic radii from chlorine to bromine to iodine. this trend is consistent with the general periodic trend of increasing atomic size down a group.
in summary, the bond length of a diatomic molecule in the halogen group increases as you move from chlorine to iodine. this is due to the increase in atomic size, which directly influences the bond length, making i-i bond length greater than br-br, and br-br bond length greater than cl-cl. thus, all statements given in the question are correct as they correctly reflect the trend in bond length among halogen diatomic molecules based on the atomic radii of the halogens involved.
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