Your third line,
RA is # of atoms *natural abundance of isotope 1/nat. abund. of isotope 2
is true only for a single atom of the element.
In general case, the theoretical RA values are derived from probability theory, and are of the form
of the binomial expansion,
(a + b) to the nth power, where a is nat. abund. of isotope 1
b .. 2
and n is the number of atoms of that element.
For example, 35Cl = about 72 % RA, and 37Cl = about 24 % RA (numbers approximated to make the calculation more obvious)
For Cl2, a = 0.72, b = 0.24, n = 2
So, (a + b) squared = a sqd + 2ab + b sqd = ratio is 0.5184:0.3360:0.0576
= 9:6:1 approximately
Here, n = 1 for Si but n = 3 for C, and n = 9 for H.
m/z 73 = (CH3)3Si, so m/z 75 = 12C3 1H9 30Si, RA = 3.36 %
and also m/z 75 = 13C2 12C1 1H9 28Si
ratio = (a + b) cubed, where a = 98.90, b = 1.10 % and n = 3 C atoms.[see calc. below]
You can see that the 13C3 contribution (0.00014%) IS negligible compared to the 30Si contribution (3.36%).
for m/z 74 = 29Si gives 5.06 % RA
and also m/z 74 = 13C1 12C2 1H9 28Si, (a + b) to nth power gives
(a cubed )+ (3* a sqd *b )+ (3 * b sqd * a) + (b cubed), since n = 3 C atoms
a = 98.9%, b = 1.10%
so ratio m/z 73:74:75 is 967362:32278 + 359:1.331 = 100:3.37:0.00014.
These probabilities are independent of each other, so are additive.
So if m/z 73 =100 % (base peak),
then m/z 74 = 5.06 for 29Si + 3.37 for the 13C1 12C2 = 8.43%.
The calculation given by the solutions manual is I believe INCORRECT, since the natural relative abundances of the elements, and therefore the probabiliites of occurrence, are independent of each other.
Your calculation for 30Si = 3.36% should be correct.
It has been quite a few yrs since I have had to grind this out, line by line, so have someone else check it.