Productivity is the rate of production of biomass expressed in terms of
(i) `("kcal"m^(-3))yr^(-1)`
(ii) `g^(-2)yr^(-1)`
(iii) `g^(-1)yr^(-1)` (iv) `("kcal"m^(-2))yr^(-1)`

Options

A. ii
B. iii
C. ii and iv
D. I and iii

Explanation

To solve the question regarding the units of productivity, we need to understand what productivity means in the context of an ecosystem. Productivity is the rate at which biomass is produced in a given area over a specific time period. It can be expressed in terms of energy or weight.

### Step-by-Step Solution:

1. **Understanding Productivity**:
- Productivity refers to the rate of production of biomass in an ecosystem. It can be measured in terms of energy (like kilocalories) or mass (like grams).

2. **Identifying Units**:
- The units of productivity can be expressed in various forms. The options given are:
- (i) `("kcal"m^(-3))yr^(-1)`
- (ii) `g^(-2)yr^(-1)`
- (iii) `g^(-1)yr^(-1)`
- (iv) `("kcal"m^(-2))yr^(-1)`

3. **Analyzing Each Option**:
- **Option (i)**: `("kcal"m^(-3))yr^(-1)` - This suggests energy per volume, which is not typical for measuring productivity, as productivity is usually measured per area.
- **Option (ii)**: `g^(-2)yr^(-1)` - This suggests mass per area squared, which does not make sense in the context of productivity.
- **Option (iii)**: `g^(-1)yr^(-1)` - This suggests mass per area, but the unit is not commonly used for productivity.
- **Option (iv)**: `("kcal"m^(-2))yr^(-1)` - This suggests energy per area, which is a standard way to express productivity in terms of energy.

4. **Selecting the Correct Options**:
- Based on the analysis, the correct unit for productivity in terms of weight is option (iii) `g^(-1)yr^(-1)`, and in terms of energy, it is option (iv) `("kcal"m^(-2))yr^(-1)`.
- Therefore, the correct answers are (iii) and (iv).

5. **Final Conclusion**:
- The units that correctly express productivity are `g^(-1)yr^(-1)` for biomass and `("kcal"m^(-2))yr^(-1)` for energy.