Given below are two statements:

Statement I: The primary source of energy in an ecosystem is solar energy.

Statement II: The rate of production of organic matter during photosynthesis in an ecosystem is called net primary productivity (NPP).

In the light of the above statements, choose the most appropriate answer from the options given below:

The correct option is: Statement I is correct but statement II is incorrect.

Let us analyze the two statements step-by-step to understand why this is the correct choice:

Analysis of Statement I:
Statement I states: "The primary source of energy in an ecosystem is solar energy."
Solar energy (sunlight) is the ultimate and primary source of energy for almost all ecosystems on Earth. Green plants (producers) capture solar energy and convert it into chemical energy through photosynthesis, which then flows through various trophic levels (herbivores, carnivores, etc.) in the food chain. Therefore, Statement I is correct.

Analysis of Statement II:
Statement II states: "The rate of production of organic matter during photosynthesis in an ecosystem is called net primary productivity (NPP)."
This statement is scientifically inaccurate. The total rate at which organic matter is created by producers during photosynthesis is called the Gross Primary Productivity (GPP). Net Primary Productivity (NPP) is the energy or organic matter that remains after accounting for the loss of energy due to respiration (R) by the plants themselves. It is represented by the relationship:
$\mathrm{NPP}=\mathrm{GPP}-\mathrm{Respiration\; losses\; (R)}$
Since the statement incorrectly defines Net Primary Productivity (NPP) instead of Gross Primary Productivity (GPP), Statement II is incorrect.

Conclusion:
Since Statement I is correct and Statement II is incorrect, the most appropriate answer is "Statement I is correct but statement II is incorrect".