# The half life of a radioactive element is 30 seconds. In what period of time would the activity of the sample be reduced to one - sixteenth of the original activity?

##### 1 Answer

#### Answer:

Working formula:

#### Explanation:

You can simplify the above working formula to the following form:

where

Now, we know that the formula for half-life (which can be obtained from the above equation itself) is given by:

So, here the half-life is

Now, using this value of

So

Therefore, the activity of the radioactive element becomes one-sixteenth of its original activity at