Step 1: Understanding the Concept
Carbon cycles through the atmosphere as \(\text{CO}_2\), but phosphorus has no significant gaseous form.
Step 2: Statement I
Carbon enters ecosystems in large amounts from the atmosphere, while rainfall brings in very little phosphorus. So statement I is correct.
Step 3: Statement II
The exchange of phosphorus between organisms and the environment is much smaller than that of carbon. So statement II is incorrect.
Final Answer:
Statement I is correct but Statement II is incorrect.
\[ \boxed{\text{(C) }\text{Statement (I) is correct but Statement (II) is incorrect.}} \]