Chemistry, 22.07.2019 03:00 sarah5557

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?

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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 gramsAfter 40 secs, 8 gramsAfter 60 secs, 4 gramsAfter 80 secs, 2 gramsAfter 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 = $\dfrac{\text A}{{2}^{\text n}}$

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 = $\dfrac{20}{20}$ = 1Amount of the substance left after 1 half life = $\dfrac{\text 32}{{2}^{\text 1}}$ = 16 grams.

2.Time = t = 40 seconds

Number of half-lives = $\dfrac{40}{20}$ = 1Amount of the substance left after 1 half life = $\dfrac{\text 32}{{2}^{\text 2}}$ = 8 grams.

3.Time = t = 60 seconds

Number of half-lives = $\dfrac{60}{20}$ = 1Amount of the substance left after 1 half life = $\dfrac{\text 32}{{2}^{\text 3}}$ = 4 grams.

4.Time = t = 80 seconds

Number of half-lives = $\dfrac{80}{20}$ = 1Amount of the substance left after 1 half life = $\dfrac{\text 32}{{2}^{\text 4}}$ = 2 grams.

5.Time = t = 100 seconds

Number of half-lives = $\dfrac{100}{20}$ = 1Amount of the substance left after 1 half life = $\dfrac{\text 32}{{2}^{\text 5}}$ = 1 grams.

To know more about half-life, refer to the following link:

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Answer from: midhin

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 from: Quest

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The half-life of the radioactive element unobtanium dash 53 is 20 seconds. if 32 grams of unobtanium...

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