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Dear Puneet,
The formula that we use to calculate the half time is t = ln 2 / λ has many approximations. First approximation is the value of ln 2 which is usually taken as 0.693 which is only an approximate value and the decay constant usually measured from the experiments are also approximate. And thus the value of half time we get is also an approximate value. The concept of half life essentially an aid for understanding the phenomena of radioactive deacay of aprent nucleus. Also it has some applications like that of carbon dating and uranium dating for determinig the ages of organic matters and the age of the earth. Also the values of the half life are in the orders of usally thousands of years in these applications. Another important thing is that there are no such thing as 5 atoms , usually in all radioactivity measurements they are present in the orders of millions atleast. Dont look at the concept as a simple mathematical concept.
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Adapa Bharath
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