$2.)$ We have $20$nmol of DNA with the below sequence in $5mL$ of buffer. We heat the sample to denature the DNA. We are interested in the reassociation kinetics of the BamHI restriction site, which is present in the DNA sequence.

DNA sequence:

$5\text{'}-$

AGCTTTGAAGGATCCATTATAGCGCACTTTGACCACCT AAATGATGGAAAATAGGGGCATCAGGATCCTATA$-3\text{'}$

$3\text{'}-$

TCGAAACTTCCTAGGTAATATCGCGTGAAACTGGTGGA TTTACTACCTTTTATCCCCGTAGTCCTAGGATAT$-5\text{'}$

BamHI restriction site:

$5^{\text{'}}-$ GGATCC $-3\text{'}$

$3^{\text{'}}-$ CCTAGG $-5\text{'}$

$($a$)$ Calculate the concentration $A_0$ of BamHI base pairs in the initial DNA sample.

$($b$)$ We are performing the DNA renaturation reaction under standard conditions for this type of experiment. At $t=25sec,$ calculate the fraction of DNA renatured $(f).$ The $2^{nd}$ order rate constant $(k_2)$ for this renaturation reaction is $63188M^{-1}se{c}^{-1}.$

$($c$)$ Calculate the time $($t$)$ at which half of the DNA strands have reassociated in this reaction $)=(0\mathrm{.}5.$