According to crystal field theory d-orbitals split up in octahedral field into two sets.`d_("xy")d_("yx")d_("zx")` have lower energy and `d_(x^(2)-y^(2))" "and" "d_(z^(2))` have higher energy. The difference in energy of these two sets of d-orbitals is called crystal field splitting energy denoted by `Delta_(0)`.
In tetrahedral field `d_(x^(2)-y^(2))" "and" "d_(z^(2)` have lower energy whereas `d_("xy")d_("yz")d_("zx")` have higher energy. The difference in energy is denoted `Delta_(t)`.
`Delta_(0)` can be determined by measuring `lambda_("max")` for absorption and converting into energy units. `Delta_(0)` depends upon nature of metal ions as well as nature of ligands. The magnitude of `Delta_(0)` also decides low energy levels are filled.
Given the following data about absorption maximum of several complex ions, the correct order of `Delta_(0)` for these ions is
Complexes `lambda_("max")`
`[Cr(H_(2)O)_(6)]^(3+) 694 "nm"`
`[Cr(NH_(3))_(6)]^(3+) 465"nm"`
`[CrC1_(6)]^(3-)" "758 "nm"`

Options

A. `Delta_(0)[Cr(NH_(3))_(6)]^(3+)gt Delta_(0)[Cr(H_(2)O)_(6)]^(3+)gtDelta_(0)[CrC1_(6)]^(3-)`
B. `Delta_(0)[Cr(NH_(3))_(6)]^(3+)= Delta_(0)[Cr(H_(2)O)_(6)]^(3+)gtDelta_(0)[CrC1_(6)]^(3-)`
C. `Delta_(0)[Cr(NH_(3))_(6)]^(3+)lt Delta_(0)[Cr(H_(2)O)_(6)]^(3+)ltDelta_(0)[CrC1_(6)]^(3-)`
D. `Delta_(0)[Cr(N_(2)O)_(6)]^(3+)gt Delta_(0)[CrC1_(6)]^(3-)gtDelta_(0)[Cr(NH_(3))_(6)]^(3+)`

Answer

a

Explanation

`Delta_(0) = ("hc")/(lambda)`