Recognitions:
 Quote by Sekonda Upon using more accurate values I attain $$n-\delta_{i}=8.33$$
Then you are still not using values which are accurate enough. Using the values given in the exercise I get $$n-\delta_{i}=8.1286$$ which is a rather good match.
 Using the planck constant as 6.626*.... and the speed of light as 2.99*.... I get that $$n-\delta_{i}=8.0094$$ so maybe it's a d-orbital of the n=8 level?