4. (a) Derive an expression for the half-life of the reactant in a first-order process in terms of the rate constant k. (b) Find the natural lifetime for first-order reactions corresponding to half-life = 26.5 years. (20%)

4. Please translate the following paragraph into Mandarin. Double-stranded breaks (DSBs) in DNA arise frequently. If these breaks are not repaired, the consequence to the cell is disastrous. For example, a single DSB in the Escherichia coli chromosome is lethal to a cell that lacks the ability to repair it. The major mechanism used to repair DSBs in most cells is homologous recombination. Some cell types also use a simpler mechanism, such as nonhomologous end joining (NHEJ) to heal their chromosomes.

4. (a) Derive an expression for the half-life of the reactant in a first-order process in terms of the rate constant k. (b) Find the natural lifetime for first-order reactions corresponding to half-life = 26.5 years. (20%)

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