The characteristics of radioactive decay are studied under various conditions. Which of the following statements correctly describe these characteristics?

1. The activity of a radioactive sample is unaffected by its chemical bonding environment, pressure, or temperature.
2. Since the half-life $T_{1/2}$ is inversely proportional to the decay constant $\lambda$, isotopes with larger decay constants decay more slowly.
3. A plot of the activity of a sample against the number of remaining undecayed nuclei is a straight line passing through the origin.

A. 1 only B. 1 and 3 only C. 2 and 3 only D. 1, 2 and 3