The DNA molecule has the shape of a double helix. The radius of each helix is about 10 angstroms (1 Å = 10−8 cm). Each helix rises about 34 Å during each complete turn, and there are about
2.9 × 108
complete turns. Estimate the length of each helix. (Round your answer to two decimal places.)
To estimate the length of each helix of the DNA molecule, we can calculate the total distance covered by each complete turn and multiply it by the number of complete turns.
1. Calculate the distance covered by each complete turn:
- The rise of each helix during each complete turn is given as 34 Å.
2. Calculate the total distance covered by each complete turn:
- Since the DNA molecule has the shape of a double helix, there are two strands. Therefore, the total distance covered by each complete turn would be twice the rise of each helix.
- 34 Å × 2 = 68 Å
3. Calculate the length of each helix:
- Multiply the total distance covered by each complete turn by the number of complete turns.
- (68 Å) × (2.9 × 10^8 complete turns) = 1.972 × 10^10 Å
4. Convert the length from angstroms to centimeters:
- 1 Å = 10^(-8) cm
- Divide the length by the conversion factor to get the length in centimeters.
- (1.972 × 10^10 Å) × (10^(-8) cm/Å) = 1.972 cm
Therefore, the estimated length of each helix of the DNA molecule is approximately 1.972 cm.