I was provided with the following structure of an inorganic metal complex:
And asked to give information on its NMR spectrum shown below
The highfield signal is caused by a singlet with Platinum ($I = \frac{1}{2}$) due to the terminal $\ce{CH3}$ groups.
As $\ce{^{195}Pt}$ has an abuance of $33.8\%$ this meant that in $66.2\%$ of cases, the singlet will not split, whereas in around $33.8\%$ of cases a doublet would be observed due to the satellites, which would have intensities of $\frac{33.8}{2} = 16.9\%$ hence the "Triplet" was in the ratio of around $16:67:16$.
The low-field signal however for me was easy to deduce but more difficult to calculate ratios for. The Methyl's could couple to
- No $\ce{^{195}Pt}$ resulting in a singlet
- One $\ce{^{195}Pt}$ resulting in a doublet
- Two $\ce{^{195}Pt}$ resulting in a singlet
The calculations given in the answer are shown:
- No $\ce{^{195}Pt}$ resulting in a singlet: intensity $0.66 \times 0.66$
- One $\ce{^{195}Pt}$ resulting in a doublet: intensity $2 \times 0.66 \times 0.33$
- Two $\ce{^{195}Pt}$ resulting in a singlet: intensity $0.33 \times 0.33$ This results in a final ratio of 1:8:18:8:1
These calculations confused me. Why would for a singlet, the intensity be $0.66 \times 0.66$ if both $\ce{CH3}$ give the same signal and hence for the doublet would I need to multiply $0.66 \times 0.33$ by $2$?
These calculations also seemed erroneous. The calculation for the intensity of the doublet and singlet give the exact same answer and I could not reach the final ratio.
What is the logic behind these calculations?