Final answer:
To calculate the number of grams of ^35S in a sample with a given decay rate, we need to use the decay rate equation and the half-life formula. We can then convert the number of nuclei to grams using the molar mass of ^35S.
Step-by-step explanation:
To calculate the number of grams of ^35S in a sample with a given decay rate, we need to use the equation: R = λN, where R is the decay rate, λ is the decay constant, and N is the number of nuclei. Rearranging the equation, we have N = R / λ. The decay constant λ can be found using the half-life formula λ = ln(2) / T1/2, where T1/2 is the half-life. Plugging in the values given in the question, we can calculate the decay constant λ. Once we have the decay constant λ, we can use the equation N = R / λ to find the number of ^35S nuclei. Finally, we can convert the number of nuclei to grams by using the molar mass of ^35S.