Question

The​ half-life of the radioactive element unobtanium dash 53 is 20 seconds. if 32 grams of unobtanium dash 53 are initially​ present, how many grams are present after 20 ​seconds? 40 ​seconds? 60 ​seconds? 80 ​seconds? 100 ​seconds?

Answer 1

Answer: After 20 seconds, 16 grams of unobtanium will be present, after 40 seconds, 8 grams of unobtanium will be present after 60 seconds, 4 grams of unobtanium will be present, after 80 seconds, 2 grams of unobtanium will be present and after 100 seconds, 1 grams of unobtanium will be present.

Explanation: Half life is the time in which half of the reaction is completed. Thus the half of the substance will be decomposed and half of it will remain.

Amount of the substance left after n half lives will be=$\frac{A}{2^n}$

where A= initial amount of substance

n=no of half lives=$\frac{\text{given time}}{\text{half life}}$

a) t= 20 seconds

no of half lives=$\frac{20}{20}=1$

amount of the substance left after 1 half life will be=$\frac{32}{2^1}$=16 g.

b)  t= 40 seconds

no of half lives=$\frac{40}{20}=2$

amount of the substance left after 2 half lives will be=$\frac{32}{2^2}$=8g.

c) t= 60 seconds

no of half lives=$\frac{60}{20}=3$

amount of the substance left after 3 half lives will be=$\frac{32}{2^3}=4g$

d) t= 80 seconds

no of half lives=$\frac{80}{20}=4$

amount of the substance left after 4 half lives will be=$\frac{32}{2^4}=2g$

e) t= 100 seconds

no of half lives=$\frac{100}{20}=5$

amount of the substance left after 5 half lives will be=$\frac{32}{2^5}=1g.$

Answer 2

when the half-life is the amount of time which the radioactive isotopes need to

be in half.

So when w start with 32 g of unobtanium 53 so :

1- after 20 sec the number of grams remain = 32/2

                                                       = 16 g

2- and after 40 sec the number of grams remain

16 g will cut in half:

= 16 / 2 

= 8 g

3- and after 60 sec the number of grams remain

8 g will cut in half:

= 8g /2

= 4 g

4- and after 80 sec the number of grams remain

4 g will cut in half:

= 4 g /2

 = 2 g

5-after 100 sec the number of grams remain

2 g will cut in half :

     = 2g /2 

     = 0 g

after 100 sec there are no grams remain