`DNA` has density `1.1 g//mL`. And its molecular weight is `6xx10^(3) g//"mol"`. Average volume occupied by its single molecule will be :

Options

A. `9.1 xx 10^(-20) cc`
B. `9.1 xx 10^(-21) cc`
C. `9.8 xx 10^(-24) cc`
D. `9.6 xx 10^(-28) cc`

Answer

To find the average volume occupied by a single molecule of DNA, we can follow these steps:

### Step 1: Determine the mass of one molecule of DNA
Given the molecular weight of DNA is \(6 \times 10^3 \, \text{g/mol}\), we can find the mass of one molecule using Avogadro's number (\(N_A = 6 \times 10^{23} \, \text{mol}^{-1}\)).

\[ \text{Mass of one molecule} = \frac{\text{Molecular weight}}{N_A} = \frac{6 \times 10^3 \, \text{g/mol}}{6 \times 10^{23} \, \text{mol}^{-1}} = 10^{-20} \, \text{g} \]

### Step 2: Use the density to find the volume occupied by one molecule
The density of DNA is given as \(1.1 \, \text{g/mL}\). We can use the relationship between mass, volume, and density, which is given by the formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Substituting the mass of one molecule and the density into the formula:

\[ \text{Volume of one molecule} = \frac{10^{-20} \, \text{g}}{1.1 \, \text{g/mL}} = \frac{10^{-20}}{1.1} \, \text{mL} \approx 9.1 \times 10^{-21} \, \text{mL} \]

### Final Answer
The average volume occupied by a single molecule of DNA is approximately \(9.1 \times 10^{-21} \, \text{mL}\).

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