# Logic Puzzle #9: Does my Unknown contain Br, Cl, S and/or Si atoms? … Solution 2

##### November 25, 2010

Atoms like Br, Cl, S and Si present distinct isotope patterns on a mass spectrum. The isotope pattern for a single Br or Cl atom tends to be relatively straightforward and can be viewed directly off the spectrum. In the case for S and Si atoms, a little math is generally required to reveal their presence or absence.

The careful analysis of the intensity for the A+2 signal (m/z 156.0) at 13 eV offers a good notion as to whether any of the following atoms Br, Cl, S or Si are present. The contributions of the isotopes 81Br, 37Cl, 34S and 30Si to the A+2 signal are related to the isotope-abundance and are listed by IUPAC at ~49.3, 24.2, 4.2 and 3.1%, respectively. Please note that the contributions to the A+2 signal from 13C2, 13C80Br, 13C36Cl, 13C33S and 13C30Si will be considered ~0.0% to simply the calculations.

Since the intensity of the A signal (m/z 154.0) is 78.3% at 13 eV, then the intensity of the A+2 signal will be the following if the corresponding atom(s) is present:

1 Br ~76.1% (=78.3*1*49.3/(100-49.3))

2 Br ~152.3% (=78.3*2*49.3/(100-49.3))

1 Cl ~25.0% (=78.3*1*24.2/(100-24.2))

2 Cl ~50.0 % (=78.3*2*24.2/(100-24.2))

1 S ~3.4% (=78.3*1*4.2/(100-4.2))

2 S ~6.9% (=78.3*2*4.2/(100-4.2))

1 Si ~2.5% (=78.3*1*3.1/(100-3.1))

2 Si ~5.0% (=78.3*2*3.1/(100-3.1))

According to the calculations, Br, Cl, S and Si are not present as they do not match the experimental intensity of the A+2 signal at 1.0%.

Formula:

1. % Intensity of A+2 signal = % Intensity of A signal * (Contribution of a+2X + Contribution of 13C2 + Contribution of 13Ca+1X + …)

2. Contribution of Isotope = Number of Atoms * % abundance / (100 – % abundance)