An observer in a laboratory starts with `N_(0)` nuclei of a radioactive sample and keeps on observing the number (N) of leftover nuclei at regular intervals of 10 minutes each. She prepares the following table on the basis of her observation.

Use this data to plot a graph of `log_(e)(N_(0)//N)` vs time (t) and calculate the
(a) decay constant
(b) half-life of the given sample.

Explanation

The graph between `log_(e) (N_(0)//N)` and time t is plotted as below:

(a) We know that
`log_(e)N_(0)/N = lambda t`
`rArr lambda =1/t log e N_(0)/N`
When t = 10 min.
`log_(e)(N_(0)/N) = 3.465` (from graph)
`therefore lambda =1/10 xx 3.465 = 0.3465 min^(-1)`
(b) Half-life,
`T_(1//2) = 0.693/lambda = 0.693/0.3465 =2` minutes.