**Question 4:**A 1.00 g sample of $^ {66}_{32}\text{Ge}$ decays to 0.87 g in 1.9 hours. What is the half-life of $^ {66}_{32}\text{Ge}$?- a. 0.073 hr- b. 0.11 hr- c. 4.5 hr- d. 9.5 hr- e. 14 hrThis question examines your understanding of radioactive decay and half-lives. It asks you to calculate the half-life of a substance based on its decay rate over a given period. The options provide several possible half-life durations in hours.

Decay reactions are first order reactions. Given : Initial mass of reactant = 1.00 g Final mass of reactant remaining = 0.87 g And time taken = 1.9 hr Since we know that the relationship between the amount of reactant i.e [A] and time for a first order reaction is given by => ln{[A]0[A]} = Kt where [A] = final amount of reactant = 0.87 g [A]0 = initial amount of reactant = 1.00 g t = time = 1.9 hr K = Rate constant Hence substituting the values we get, => ln1.000.87 = K X 1.9 => K = Rate constant = 0.0733 hr-1 approx. Hence the half life of the first order reaction is given by, => Half life = ln(2)K = ln(2)0.0733 = 9.5 hr approx. Hence the answer is option d. 9.5 hr.

Answered: A 1.00 g sample of Ge decays to 0.87 g…

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A 1.00 g sample of Ge decays to 0.87 g in 1.9 hr. What is the half-life of Ge ? 32 a. 0.073 hr b. 0.11 hr c. 4.5 hr d. 9.5 hr 14 hr е.

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