Answer
A) DNA molecule = 1.6 mm; This is clearly much longer than the length of a cell, so the DNA must be heavily coiled to fit within the cell.
B) Maximum number of proteins = 3,920 proteins
Work Step by Step
A) Divide the molecular weight of a DNA molecule by the average molecular weight of a nucleotide pair to determine how many nucleotides are in a DNA molecule. Then multiply by the length of a single nucleotide to find the length of the DNA:
($3.1x10^9$ g⁄mol)/($660$ g⁄mol)$ = 4.7x10^6$ nucleotides
$4.7x10^6$ nucleotides $* 0.34x10^-9$ m $= 1.6$ mm
B) Use the knowledge that three nucleotides = 1 codon = 1 amino acid to convert the total number of nucleotides to the maximum number of proteins:
$4.7x10^6$ nucleotides$* (1$ codon)$/(3$ nucleotides$)* (1 $amino acid)/codon)$*(1$ protein)$/(400$ amino acids) $=3,920$ proteins or $\approx 4000$ proteins
