GATE 2023 BT – Question 56
If 1000 bp of double-helical DNA weighs $1\times10^{-18}$ g and the distance between two bp is 0.34 nm, the DNA mass (mg, one decimal place) required to stretch the Earth–Moon distance of 3,74,000 km is ___________.
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Correct answer: 1.09 to 1.11
Explanation
**Step 1: number of base pairs needed.** The Earth-Moon distance is $374\,000\text{ km}=3.74\times10^{5}\times10^{3}\text{ m}=3.74\times10^{8}\text{ m}$. In nm that is $3.74\times10^{17}$ nm. Each base pair adds 0.34 nm:
$$N=\frac{3.74\times10^{17}}{0.34}=1.1\times10^{18}\text{ bp}.$$
**Step 2: mass per base pair.** 1000 bp weigh $1\times10^{-18}$ g, so 1 bp weighs $10^{-21}$ g.
**Step 3: total mass.**
$$m=1.1\times10^{18}\times10^{-21}\text{ g}=1.1\times10^{-3}\text{ g}=\mathbf{1.1\ mg}.$$