We are given several questions related to DNA and RNA molecules. We need to answer the following questions: a. In a human cell, every DNA molecule has $6 \times 10^9$ nucleotides. What is the total length in millimeters? b. How is it possible that these lengths can shrink and be inside a cell nucleus which has a diameter of only 2-3 thousandths of a millimeter? c. One single chain of a DNA molecule has $3 \times 10^4$ nucleotides. If a DNA molecule replicates twice, how many free nucleotides are needed? d. In a DNA molecule, cytosine nucleotides are equal to 14% of the total number of nucleotides. Calculate the number of each type of nucleotide in the DNA molecule. e. This DNA molecule can be used as a template. How many mRNA molecules are needed if each mRNA molecule has an average of $10^4$ nucleotides?

1. Problem Description

We are given several questions related to DNA and RNA molecules. We need to answer the following questions:

a. In a human cell, every DNA molecule has $6 \times 10^9$ nucleotides. What is the total length in millimeters?

b. How is it possible that these lengths can shrink and be inside a cell nucleus which has a diameter of only 2-3 thousandths of a millimeter?

c. One single chain of a DNA molecule has $3 \times 10^4$ nucleotides. If a DNA molecule replicates twice, how many free nucleotides are needed?

d. In a DNA molecule, cytosine nucleotides are equal to 14% of the total number of nucleotides. Calculate the number of each type of nucleotide in the DNA molecule.

e. This DNA molecule can be used as a template. How many mRNA molecules are needed if each mRNA molecule has an average of $10^4$ nucleotides?

2. Solution Steps

a. We need to find the total length in millimeters.

The image does not provide the length of a single nucleotide. Hence, it is impossible to determine the total length.

b. The DNA molecule is tightly packaged and coiled around proteins called histones to form chromatin, which can then be further condensed into chromosomes. This process allows the long DNA molecule to fit within the small volume of the cell nucleus.

c. If a DNA molecule replicates twice, it means that one DNA molecule becomes four DNA molecules.

Since one single chain of a DNA molecule has $3 \times 10^4$ nucleotides, the total number of nucleotides in one DNA molecule is $2 \times 3 \times 10^4 = 6 \times 10^4$.

When replicating twice, we get four DNA molecules, each requiring $6 \times 10^4$ nucleotides.

Total nucleotides needed = $3 \times 6 \times 10^4 = 18 \times 10^4 = 1.8 \times 10^5$

The initial DNA molecule already uses $6 \times 10^4$, thus we need $3 * 6 * 10^4 = 1.8 \times 10^5$ free nucleotides.

d. In a DNA molecule, Cytosine (C) = 14% of total nucleotides. Since C = G and A = T, Guanine (G) = 14%.

Therefore, A + T = 100% - 14% - 14% = 72%.

A = T = 72%/2 = 36%.

Number of nucleotides:

C = 14% * $(6 \times 10^4) = 0.14 \times 6 \times 10^4 = 0.84 \times 10^4 = 8400$

G = 14% * $(6 \times 10^4) = 0.14 \times 6 \times 10^4 = 0.84 \times 10^4 = 8400$

A = 36% * $(6 \times 10^4) = 0.36 \times 6 \times 10^4 = 2.16 \times 10^4 = 21600$

T = 36% * $(6 \times 10^4) = 0.36 \times 6 \times 10^4 = 2.16 \times 10^4 = 21600$

e. The single DNA strand has $3 \times 10^4$ nucleotides.

Total number of nucleotides in one DNA molecule $= 2 \times 3 \times 10^4 = 6 \times 10^4$

Each mRNA molecule has $10^4$ nucleotides.

Number of mRNA molecules needed $= \frac{3 \times 10^4}{10^4} = 3$

Since the problem states it needs mRNA copies produced from a single template strand, then the solution is $3 \times 10^4$ divided by the number of nucleotides on each mRNA molecule which is $10^4$.

3. Final Answer

a. Insufficient information to answer.

b. The DNA molecule is tightly packaged and coiled around proteins called histones to form chromatin.

c. $1.8 \times 10^5$ free nucleotides are needed.

d. C = 8400, G = 8400, A = 21600, T = 21600

e. 3 mRNA molecules are needed.