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Chapter 22: Problem 146

The average molar mass of one base pair of nucleotides in DNA is approximately 600 g/mol. The spacing between successive base pairs is about $0.34 \mathrm{nm},$ and a complete turn in the helical structure of DNA occurs about every 3.4 \(\mathrm{nm}\) . If a DNA molecule has a molar mass of $4.5 \times 10^{9} \mathrm{g} / \mathrm{mol}$ , approximately how many complete turns exist in the DNA \(\alpha\) -helix structure?

Short Answer

Expert verified
There are approximately 750,000 complete turns in the DNA 𝛼-helix structure.

Step by step solution

01

Calculate the number of base pairs

To calculate the number of base pairs in the DNA molecule, we divide the molar mass of the DNA molecule by the average molar mass of one base pair. We can write this as: Number of base pairs = (Molar mass of DNA molecule) / (Average molar mass of one base pair) Number of base pairs = (4.5 * 10^9 g/mol) / (600 g/mol) Number of base pairs ≈ 7.5 * 10^6
02

Calculate the length of the DNA molecule

Now, we will find the length of the DNA molecule. For this, we will multiply the number of base pairs by the spacing between successive base pairs: Length of DNA molecule = (Number of base pairs) * (Spacing between successive base pairs) Length of DNA molecule ≈ (7.5 * 10^6) * 0.34 nm Length of DNA molecule ≈ 2.55 * 10^6 nm
03

Calculate the number of complete turns

Finally, we need to determine how many complete turns exist in the DNA 𝛼-helix structure. To do this, we will divide the length of the DNA molecule by the length per turn: Number of complete turns = (Length of DNA molecule) / (Length per turn) Number of complete turns ≈ (2.55 * 10^6 nm) / (3.4 nm) Number of complete turns ≈ 750,000 So, there are approximately 750,000 complete turns in the DNA 𝛼-helix structure.

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