Question

The length of a double helical DNA molecule is 13.6 km. If the DNA double helix weighs $1 \times 10^{-18}$ g per 1000 nucleotide pairs and rise per base pair is 3.4 Å, then weight of the double helical DNA molecule (in nanogram) will be _______ (in integer).

Hint:

Always convert DNA length to Å, then divide by 3.4 Å per base pair. Multiply total base pairs by weight per bp to find DNA mass.

Answer 1

Step 1: Convert DNA length. Length = 13.6 km = $13.6 \times 10^3$ m = $1.36 \times 10^7$ mm = $1.36 \times 10^{10}$ µm = $1.36 \times 10^{11}$ Å. 
Step 2: Calculate number of base pairs. Rise per base pair = 3.4 Å. \[ \text{Number of bp} = \frac{1.36 \times 10^{11}}{3.4} \approx 4 \times 10^{10}. \] Step 3: Weight per 1000 bp. Given = $1 \times 10^{-18}$ g per 1000 bp $⇒ 1 \times 10^{-21}$ g per bp. 
Step 4: Total weight. \[ \text{Weight} = 4 \times 10^{10} \times 1 \times 10^{-21} \, g = 4 \times 10^{-11} g. \] Step 5: Convert to nanograms. $1$ g = $10^9$ ng. \[ 4 \times 10^{-11} g = 40 \, \text{ng}. \] Final answer = 40 ng.