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 contains 10% cytosine, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Length of DNA to Meters**:
- The length of the DNA sample is given as 13.6 nm.
- To convert nanometers to meters, we use the conversion factor:
\[ 1 \text{ nm} = 10^{-9} \text{ m} \]
- Therefore:
\[ 13.6 \text{ nm} = 13.6 \times 10^{-9} \text{ m} \]

2. **Determine the Number of Base Pairs**:
- The distance between one base pair in DNA is approximately 0.34 nm (or 3.4 Å).
- To find the number of base pairs in the DNA, we divide the total length of the DNA 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 Percentage of Cytosine and Guanine**:
- It is given that 10% of the bases are cytosine (C).
- Since cytosine pairs with guanine (G), there will also be 10% guanine.
- Therefore, the total percentage of C and G is:
\[ 10\% + 10\% = 20\% \]

4. **Calculate the Number of C-G Base Pairs**:
- The number of C-G base pairs can be calculated as:
\[ \text{Number of C-G pairs} = 20\% \text{ of total base pairs} = \frac{20}{100} \times 40 = 8 \]

5. **Calculate the Number of Hydrogen Bonds from C-G Pairs**:
- Each C-G pair forms 3 hydrogen bonds.
- Therefore, the total number of hydrogen bonds from C-G pairs is:
\[ \text{Hydrogen bonds from C-G} = 8 \times 3 = 24 \]

6. **Calculate the Percentage of Adenine and Thymine**:
- The remaining percentage of bases (A and T) is:
\[ 100\% - 20\% = 80\% \]
- This means there are 40% adenine (A) and 40% thymine (T).

7. **Calculate the Number of A-T Base Pairs**:
- The number of A-T base pairs can be calculated as:
\[ \text{Number of A-T pairs} = 80\% \text{ of total base pairs} = \frac{80}{100} \times 40 = 32 \]

8. **Calculate the Number of Hydrogen Bonds from A-T Pairs**:
- Each A-T pair forms 2 hydrogen bonds.
- Therefore, the total number of hydrogen bonds from A-T pairs is:
\[ \text{Hydrogen bonds from A-T} = 32 \times 2 = 64 \]

9. **Calculate the Total Number of Weak Hydrogen Bonds**:
- Finally, we add the hydrogen bonds from C-G pairs and A-T pairs:
\[ \text{Total hydrogen bonds} = 24 + 64 = 88 \]

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