CO stretching frequency band in the IR spectrum for tetracarbonylnickel and tetracarbonylferrate(II)

A past exam question says: 



> 
> With reference to the main bonding interactions between a transition
>  metal and a terminal $\ce{CO}$ ligand, explain whether you would expect to
>  observe a lower $\ce{CO}$ stretching frequency band in the infrared
>  spectrum for $\ce{[Ni(CO)4]}$ or for $\ce{[Fe(CO)4]^{2-}}$
> 
> 
> 


My attempt at an answer is:



> 
> There are essentially two bonding interactions at play in the carbonyl
>  ligand: a ligand-to-metal $\ce{n → d\sigma}$ interaction and a
>  metal-to-ligand ${d\pi → \pi^\*}$ interaction. The latter interaction is
>  called backbonding, because the metal donates electron density back to
>  the ligand.
> 
> 
> 


Nickel is further right in the periodic table than Iron, so $\ce{[Ni(CO)4]}$ has a greater stretching frequency (a greater $\ce{C–O}$ bond order). This is due to the periodic trend in orbital energy. As we move left to right across the periodic table, the $\ce{d}$ orbital energies decrease and the energies of the $\ce{d\pi}$ and ${d\pi^\*}$ orbitals separate. As a result, the backbonding orbital interaction is worse in $\ce{[Fe(CO)4]^{2-}}$ (as strong orbital interactions require well-matched orbital energies)." This means that the ${\pi^\*}$-orbitals of the $\ce{CO}$ ligands are significantly more populated in $\ce{[Fe(CO)4]^{2-}}$, so the $\ce{CO}$ bond is accordingly weakened and $\ce{v(CO)}$ is reduced.


Is this correct? 


