Question

150.0 grams of an isotope with a half-life of 36.0 hours is present at time zero. How long will it take

to decay to 18.75g?

Answer 1

Given :

Initial mass , a = 150 gm .

Half time ,

`t_{(1)/(2)}=36 \ hours`.

Final mass , x = 18.75 gm .

To Find :

The time taken to decay 18.75 gm .

Solution :

We know , time taken is given by :

`t=(1)/(k)* ln((a)/(a-x))`

Here , k is a constant given by :

`k=\frac{0.693}{t_{(1)/(2)}}\\\\\\k=(0.693)/(36)`

Putting all given value in above equation :

We get :

`t=(36)/(0.693)* ln((150)/(150-18.75))\\\\t=6.94\ hours`

Therefore , time taken is 6.94 hours .

Hence , this is the required solution .