Question

Element X decays radioactively with a half life of 6 minutes. If there are 790 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 35 grams?

Answer 1

Answer:

It takes 27 minutes for the element to decay to 35 grams

Step-by-step explanation:

Given:

Initial amount  =  790 grams

Final amount =  35 grams

Half life =  6 minutes

To find:

Time taken for the element to reduce into 35 grams  = ?

Solutions

Time taken = $half life \times \frac{ log(\frac{ initial amount}{final amount})}{log(2)}$

On substituting the values given, Time taken  

= $6 \times \frac{log(\frac{790}{35})}{log(2)}$

= $6 \times \frac{log(22.57)}{log(2)}$

= $6 \times 4.496$

= 26.97

= 27 minutes