A student got data showing productivity of three different ecosystems…

The correct answer is Option (1) → \( gm^{-2} yr^{-1} \)

Option (1) \( gm^{-2} yr^{-1} \) — Correct. Productivity is the rate of biomass production, so its unit has weight, area and time. It is expressed as g m⁻² yr⁻¹ (grams per square metre per year), or as energy, (kcal m⁻²) yr⁻¹.

Option (2) \( gm^{-3} yr^{-2} \) — Incorrect. m⁻³ is per volume, and yr⁻² is not a rate per year.

Option (3) \( (\text{Kcal}\, m^{-2}) yr^{-2} \) — Incorrect. The area is right, but time must appear once, as yr⁻¹.

Option (4) \( (\text{Kcal}\, m^{-3}) yr^{-2} \) — Incorrect. Both the area and the time units are wrong.

NCERT Extract:
Productivity – “A constant input of solar energy is the basic requirement for any ecosystem to function and sustain. Primary production is defined as the amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis. It is expressed in terms of weight (g m^–2) or energy (kcal m^–2). The rate of biomass production is called productivity. It is expressed in terms of gm^–2 yr^–1 or (kcal m^–2) yr^–1 to compare the productivity of different ecosystems.”