The length of a 13.6 km double helical DNA molecule corresponds to approximately 40 trillion base pairs, yielding a total mass of 40 micrograms when using the given parameters. The final integer mass in nanograms is 40,000 ng. This calculation aligns with standard molecular biology metrics for DNA length and mass estimation.

Introduction to DNA Dimensions

Double helical DNA maintains a consistent structure where each base pair contributes 0.34 nm (3.4 Å) to the axial length, a key parameter for calculating total nucleotide pairs from molecular length. For competitive exams like CSIR NET Life Sciences, understanding “length of double helical DNA 13.6 km” and its mass conversion proves essential. This article breaks down the query: given 13.6 km length, 1×10⁻¹⁸ g per 1000 nucleotide pairs, and 3.4 Å rise per base pair, find the DNA molecule weight in nanograms as an integer.

Step-by-Step Calculation

1. Convert 13.6 km to nanometers: 13.6 × 1000 m/km × 10⁹ nm/m = 1.36 × 10¹³ nm.
2. Divide by 0.34 nm/base pair: number of base pairs (bp) = 1.36 × 10¹³ / 0.34 = 4 × 10¹³ bp.
3. Mass per bp: (1 × 10⁻¹⁸ g / 1000 bp) = 1 × 10⁻²¹ g/bp, consistent with average ~650 g/mol per bp or ~1.02 pg per million bp scaled down.
4. Total mass: 4 × 10¹³ bp × 1 × 10⁻²¹ g/bp = 4 × 10⁻⁸ g = 40,000 ng (since 1 ng = 10⁻⁹ g). Integer answer: 40000.

Verification with Standards

Standard DNA metrics confirm 0.34 nm per base pair spacing in B-DNA helix. Mass aligns with ~618 g/mol per bp (excluding polymerization water), where 1 pg DNA ≈ 978 million bp, scaling to 10⁻²¹ g/bp here. No options provided, but result matches integer nanogram requirement for exam contexts.

CSIR NET Exam Relevance

Such problems test unit conversions and DNA structure knowledge, vital for molecular biology sections. Practice with variations: for 1.7 m DNA, bp ≈ 5 × 10⁶; mass scales proportionally. Key phrase “weight of double helical DNA molecule in nanogram” emphasizes precise computation over approximation.