To Determine: The initial amount of sample contained , which is an alpha emitter. The numbers of alpha emission are to be calculated in . The half-life of is . Answer: The number of alpha emissions occurred in are .Explanation:The kinetics followed by radioactive decay is first order. The rate constant is calculated by using the following expression. ...... (1)Here, is rate constant for the decay, is the time required, is the initial concentration and is the final concentration of reactant.For first-order reaction the relation between and rate constant is as follows; ...... (2)Here, is rate constant for the decay, is the half-life period.The rate constant for the decay is calculated by using equation (2).Substitute for ;Therefore, the rate constant for the decay is .The initial amount of the sample is .The rate constant for the decay is.Now using equation value of is calculated as;Substitute the values, for , for and for .On rearranging for ;Therefore the amount of sample remains after is .Thus the amount of sample decayed is;Therefore, the number of alpha emissions occurred in are .