Question

4. The half-life of a sample has been defined as the time it takes for half of a sample to decay. The fifth-life can be defined as the time it takes for one-fifth of a sample to decay. Given these definitions, calculate the fifth-life of a sample that has a half-life of 29 years.

Answer 1

Solution:

Since it is not mentioned specifically what is the order of the reaction thus i assume it to be a zero order reaction.

Since we know that t_1/2 for a zero order reaction is given by :-- t_1/2 = [Ao] / 2K ,where [A_o] is the initial concentration of the sample and K is the rate constant.

Since it is given that the half life period of the sample is 29 years ie, t_1/2 = 29 years.

Then, [Ao] = t_1/2 * 2K = 29*2k

Now, using the definition of fifth life, it can be mathematically given as ; t_1/5 = [Ao] / 5K

Using the evaluated value of [Ao] in the equation of fifth life, we get, t_1/5 = [Ao] / 5K = 29*2K / 5K = 11.6 years