Respuesta :
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=[tex]\frac{A}{2^n}[/tex]
where A= initial amount of substance
n=no of half lives=[tex]\frac{\text{given time}}{\text{half life}}[/tex]
a) t= 20 seconds
no of half lives=[tex]\frac{20}{20}=1[/tex]
amount of the substance left after 1 half life will be=[tex]\frac{32}{2^1}[/tex]=16 g.
b) t= 40 seconds
no of half lives=[tex]\frac{40}{20}=2[/tex]
amount of the substance left after 2 half lives will be=[tex]\frac{32}{2^2}[/tex]=8g.
c) t= 60 seconds
no of half lives=[tex]\frac{60}{20}=3[/tex]
amount of the substance left after 3 half lives will be=[tex]\frac{32}{2^3}=4g[/tex]
d) t= 80 seconds
no of half lives=[tex]\frac{80}{20}=4[/tex]
amount of the substance left after 4 half lives will be=[tex]\frac{32}{2^4}=2g[/tex]
e) t= 100 seconds
no of half lives=[tex]\frac{100}{20}=5[/tex]
amount of the substance left after 5 half lives will be=[tex]\frac{32}{2^5}=1g.[/tex]
The half-life of a radioactive element is defined as the time required by the specific isotope to decrease by half of its original value. The unobtanium after given time will be present as:
- After 20 secs, 16 grams
- After 40 secs, 8 grams
- After 60 secs, 4 grams
- After 80 secs, 2 grams
- After 100 secs, 1 gram
Half-life is the time required by the unobtanium is the half of the reaction is completed. Half of the substance will be decomposed, such that:
Amount of substance left n half-lives = [tex]\dfrac{\text A}{{2}^{\text n}}[/tex]
where A= initial amount of substance
Now,
n = number of half-lives = given time /half-life
Given,
1. Time = t = 20 seconds
- Number of half-lives = [tex]\dfrac{20}{20}[/tex] = 1
- Amount of the substance left after 1 half life = [tex]\dfrac{\text 32}{{2}^{\text 1}}[/tex] = 16 grams.
2.Time = t = 40 seconds
- Number of half-lives = [tex]\dfrac{40}{20}[/tex] = 1
- Amount of the substance left after 1 half life = [tex]\dfrac{\text 32}{{2}^{\text 2}}[/tex] = 8 grams.
3.Time = t = 60 seconds
- Number of half-lives = [tex]\dfrac{60}{20}[/tex] = 1
- Amount of the substance left after 1 half life = [tex]\dfrac{\text 32}{{2}^{\text 3}}[/tex] = 4 grams.
4.Time = t = 80 seconds
- Number of half-lives = [tex]\dfrac{80}{20}[/tex] = 1
- Amount of the substance left after 1 half life = [tex]\dfrac{\text 32}{{2}^{\text 4}}[/tex] = 2 grams.
5.Time = t = 100 seconds
- Number of half-lives = [tex]\dfrac{100}{20}[/tex] = 1
- Amount of the substance left after 1 half life = [tex]\dfrac{\text 32}{{2}^{\text 5}}[/tex] = 1 grams.
To know more about half-life, refer to the following link:
https://brainly.com/question/2057910?referrer=searchResults
