The relative density of mercury is 13.6. State its density in (i) C.G.S unit (ii) S.I. unit.

Answer

To find the density of mercury in both C.G.S and S.I. units given its relative density of 13.6, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Relative Density**:
The relative density (Rd) of a substance is defined as the ratio of the density of the substance (ρ_substance) to the density of water (ρ_water).
\[ Rd = \frac{\rho_{Hg}}{\rho_{w}} \]
For mercury, Rd = 13.6.

2. **Expressing Density of Mercury**:
Rearranging the formula gives us:
\[ \rho_{Hg} = Rd \times \rho_{w} \]

3. **Density of Water**:
We need to know the density of water. In S.I. units, the density of water is:
\[ \rho_{w} = 1000 \, \text{kg/m}^3 \]

4. **Calculating Density of Mercury in S.I. Units**:
Now substituting the values into the equation for density of mercury:
\[ \rho_{Hg} = 13.6 \times 1000 \, \text{kg/m}^3 = 13600 \, \text{kg/m}^3 \]

5. **Density of Water in C.G.S. Units**:
In C.G.S. units, the density of water is:
\[ \rho_{w} = 1 \, \text{g/cm}^3 \]

6. **Calculating Density of Mercury in C.G.S. Units**:
Now substituting the value of water density in C.G.S. units into the equation for density of mercury:
\[ \rho_{Hg} = 13.6 \times 1 \, \text{g/cm}^3 = 13.6 \, \text{g/cm}^3 \]

### Final Answers:
- (i) Density of mercury in C.G.S. units: **13.6 g/cm³**
- (ii) Density of mercury in S.I. units: **13600 kg/m³**