Chapter 2 Problems
1. Write out the equation that defines . Explain why this equation is sometimes
called a ratio of ratios.
2. Using the definition of , explain why standards have values of 0o/oo.
3. Does 0o/oo mean 0% heavy isotope, that no heavy isotope is present at all? Why
or why not? How much heavy isotope is actually present in the standards for the
HCNOS elements whose  values are 0o/oo? Table 2.1 may be of help.
4. Most natural isotope  values are 1 to 50o/oo different than isotope compositions
of standards. Use the  definition to calculate the % heavy isotope (atom percent)
for carbon samples that are -1o/oo and -50o/oo vs. the carbon standard listed
Table 2.1. (Conversion 4 in the printed Appendix gives help with this
calculation). Do these values of % heavy isotope seem similar or very different to
you? Why? Do you think it is easier to see the isotope differences using the 
notation, or when isotope values are expressed as % heavy isotope? (Hint: reading
section 2.2 may help you with this problem).
5. Explain the difference between o/o and o/oo. Why are  values given in o/oo units
and not the more familiar o/o units?
6. If a sample is enriched in heavy isotopes relative to a standard, will the  value be
positive or negative, greater than 0o/oo or less than 0o/oo? If a sample is enriched
in light isotopes relative to a standard, will the  value be positive or negative,
greater than 0o/oo or less than 0o/oo? Explain your answer.
7. If the amount of heavy isotope in a carbon sample is 0.1 percent (%) more than
that of the carbon standard listed in Table 2.1, what is the  value of the sample?
What are the  values for samples that have 1% and 10% more 13C than the
standard? What are  values for samples that have 0.1%, 1% and 10% less 13C
than the standard?
8. Commercial laboratories can separate isotopes and prepare isotope-enriched
samples. If a sample has twice the heavy isotope content of the carbon isotope
standard given in Table 2.1, what is the 13C/12C isotope ratio of this enriched
sample and what is the value for this sample?