Theoretical calculations based on crystal field theory predict that the octahedr
ID: 531658 • Letter: T
Question
Theoretical calculations based on crystal field theory predict that the octahedral complex [Rh(NH_3)_6]^3 + should have a delta_0 of 4.21 eV. Based on this prediction, what color would you expect a solution of [Rh(NH_3)_6]^3 + to be? A note on the units: the Joule is a convenient energy unit to use for hulk amounts of substance because it is derived from SI units:. However, for a single atom or molecule, a Joule is too large of a unit to be practical. For this reason, energy differences in single molecules are typically expressed in electron volts (eV). One eV is defined as the electrostatic potential energy of a single electron in a I V electric field. Look up the conversion from eV to J or better yet try' to derive it yourself!Explanation / Answer
For finding the color of the complex, the energy should be converted to its frequency units
E= h(c/l)
Where E is the energy, h is the Planks constant (6.626 × 10-34 J- s), c is the velocity of light (3*108 m/s) and l is wavelength.
It is well known that 1 eV is 1.6 * 10-19 J
Thus in our case E = 4.21 * 1.6 * 10-19 J
Substitute all these values in above equation
l = hc/E = (6.626 × 10-34*3*108) / (4.21 * 1.6 * 10-19 ) = 294.5 *10-9 m
294 nm is coming in ultraviolet region. Thus the compound will be colorless. (if any wavelength from the visible region is absorbed, then the molecule will appear colored)