The unit of Productivity in terms of energy is :

The correct answer is Option (2) → [Kcal m^-2] yr^-1

Productivity is a rate: biomass or energy made per unit area per unit time. So its unit needs area (m^-2) and time (yr^-1). In terms of energy it is kcal m^-2 yr^-1; in terms of weight, g m^-2 yr^-1.

Option (1) Kcal m^-2 — Incorrect. It has no time, so it is energy per area, not a rate.

Option (2) [Kcal m^-2] yr^-1 — Correct.

Option (3) gm^-2 yr^-1 — Incorrect. This is productivity in terms of weight, not energy.

Option (4) gm^-2 — Incorrect. Weight per area only; no time.

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.”