A compound, C20H28O, produces a 1H NMR spectrum with 11 distinct signals. The steps made by the integral trace measure 52, 17, 17, 26, 17, 25, 26, 9, 9, 35, and 8 mm. Complete the following table. Integral # Products
52 mm
17 mm
17 mm
26 mm
17 mm
25 mm
26 mm
35 mm
8 mm

Solution :

The smallest integer value represents the smaller number of protons.

In this case, in the given values, the smallest numbers are 8 mm and 9 mm, so both contains 1H each. Then next highest  value is 17 mm, which contains 1H more. Thus 17 mm contains 2H each. Then the next highest is 25 mm and 26 mm which contains 3M each and so on.

Thus the tables is :

Integral     Protons

52 mm          

17 mm            

17 mm            2

26 mm           3

17 mm            2

25 mm           3

26 mm           3

9 mm              1

9 mm              1

35 mm            4    

8 mm              1

the answer for sodium is 0.186

the answer for rubidium is 0.251