A DNA sample is 13.6 nm long . It has 10% cytosine molecules calculate the number of weak hydrogen bonds in the given sample.

Options

A. 88
B. 112
C. 80
D. 120

Answer

To solve the problem of calculating the number of weak hydrogen bonds in a DNA sample that is 13.6 nm long and has 10% cytosine, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Percentage of Other Bases**:
- Given that cytosine (C) constitutes 10%, and according to Chargaff's rules, guanine (G) will also constitute 10%.
- Therefore, the total percentage of C and G is 10% + 10% = 20%.
- The remaining percentage for adenine (A) and thymine (T) will be 100% - 20% = 80%.
- Since A and T are complementary, they will each constitute 40% (i.e., A = 40% and T = 40%).

2. **Calculate the Number of Base Pairs**:
- Each base pair in DNA is approximately 0.34 nm long.
- To find the number of base pairs in a 13.6 nm long DNA sample, we divide the total length by the length of one base pair:
\[ \text{Number of base pairs} = \frac{13.6 \text{ nm}}{0.34 \text{ nm}} \approx 40 \]

3. **Calculate the Number of Cytosine-Guanine (C-G) Base Pairs**:
- Since C and G make up 20% of the bases, we calculate the number of C-G pairs:
\[ \text{Number of C-G pairs} = 20\% \text{ of } 40 = 0.2 \times 40 = 8 \]
- Each C-G pair has 3 hydrogen bonds, so the total number of hydrogen bonds from C-G pairs is:
\[ \text{Hydrogen bonds from C-G} = 8 \times 3 = 24 \]

4. **Calculate the Number of Adenine-Thymine (A-T) Base Pairs**:
- A and T make up 80% of the bases, so we calculate the number of A-T pairs:
\[ \text{Number of A-T pairs} = 80\% \text{ of } 40 = 0.8 \times 40 = 32 \]
- Each A-T pair has 2 hydrogen bonds, so the total number of hydrogen bonds from A-T pairs is:
\[ \text{Hydrogen bonds from A-T} = 32 \times 2 = 64 \]

5. **Total Number of Hydrogen Bonds**:
- Finally, we add the hydrogen bonds from both types of pairs:
\[ \text{Total hydrogen bonds} = 24 + 64 = 88 \]

### Conclusion:
The number of weak hydrogen bonds in the given DNA sample is **88**.