Question

Question #59bcf

Answer 1

The answer is `t = 0.05 seconds`

The exponential decay of an element can be written as

`N(t) = N_0(t) * (1/2)^(t/t_(1/2))` , where

`N(t)` - the quantity that remains and has not yet decayed after a time t;
`N_0(t)` - the initial quantity of the substance that will decay;
`t_(1/2)` -the half-life of the decaying substance;

Given that `N_0(t)` = `560` grams and that we need the element to decay to `1/4` of its original mass, `N(t)` is equal to

`N_0(t) *1/4 = 140` grams

Therefore, we get `140 = 560 * (1/2)^(t/0.025)`, which yields

`140/560 = (1/2)^(t/0.025)` , and `t/0.025 = log_(1/2)(0.25)`

`t = 2* 0.025 = 0.05` seconds

Answer 2

It will take 0.05s.

A quick way is to count the number of Half-Lives which have elapsed. To go 1/2 then 1/4 of the original amount = 2 Half-Lives. So time elapsed = 2 x 0.025 = 0.05 s.

If the numbers don't work out so nicely you will need to use the method described in Stefan's answer.