Q.56 If 1000 bp of a double-helical DNA weighs 1×10−18 gm and distance between two bp is 0.34 nm, the total amount of DNA (in mg, rounded off to one decimal place) required to stretch from Earth to Moon (assuming the distance between Earth and Moon to be 3,74,000 km) is ____________.
Total DNA Amount to Stretch from Earth to Moon: 1000 bp 1×10-18 gm Calculation
The problem requires calculating the total DNA mass needed to span the Earth-Moon distance using given DNA properties. The solution involves determining base pairs needed and scaling by mass per 1000 bp.
Step-by-Step Calculation
Convert Earth-Moon distance to nanometers: 374,000 km = 374,000 × 109 nm = 3.74 × 1014 nm. Each base pair spans 0.34 nm, so total base pairs (N) = total distance / distance per bp = 3.74 × 1014 / 0.34 ≈ 1.1 × 1015 bp. Since 1000 bp weigh 1 × 10-18 g, mass per bp = 10-21 g, yielding total mass = 1.1 × 1015 × 10-21 = 1.1 × 10-6 g = 1.1 mg (rounded to one decimal).
The total amount of DNA required to stretch from Earth to Moon fascinates students tackling biophysics problems in competitive exams like IIT JAM Biotechnology. Given 1000 bp of double-helical DNA weighs 1×10-18 gm and distance between two bp is 0.34 nm, with Earth-Moon distance at 374,000 km, this query tests unit conversions and scaling.
Key Parameters Explained
- DNA mass per 1000 bp: 1 × 10-18 g establishes the scaling factor for total length.
- Bp spacing: 0.34 nm (3.4 Å) is standard B-DNA helical rise per base pair step.
- Earth-Moon distance: Specified as 3,74,000 km (3.74 × 108 m), though average is ~384,400 km—use given value for precision.
No options provided; it’s a numerical answer type (fill-in-the-blank).
Detailed Derivation
- Total length L = 3.74 × 105 km = 3.74 × 108 m = 3.74 × 1017 μm = 3.74 × 1014 nm (since 1 m = 109 nm).
- Number of bp, N = L / 0.34 nm ≈ 1.100 × 1015 bp.
- Mass of 1000 bp = 10-18 g, so mass per bp = 10-21 g.
- Total mass M = N × 10-21 g = 1.100 × 10-6 g = 1.1 × 10-3 mg? Wait, correct: 10-6 g = 10-3 mg? No—1 g = 103 mg, so 1.1 × 10-6 g = 1.1 × 10-6 × 103 = 1.1 mg.
- Rounded to one decimal: 1.1.
