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The half-life of radioactive element is 600 yr. The fraction of sample that would remain after 3000 yr is
- a)1/2
- b)1/16
- c)1/8
- d)1/32
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The half-life of radioactive element is 600 yr. The fraction of sample...
Given: Half-life of radioactive element = 600 yr
To find: Fraction of sample that would remain after 3000 yr
Solution:
We know that the half-life of a radioactive substance is the time taken for the substance to decay to half of its initial value.
Let the initial amount of the substance be 1 unit.
After 1 half-life, the amount of substance remaining = 1/2 unit
After 2 half-lives, the amount of substance remaining = (1/2) * (1/2) = 1/4 unit
After 3 half-lives, the amount of substance remaining = (1/2) * (1/2) * (1/2) = 1/8 unit
After 4 half-lives, the amount of substance remaining = (1/2) * (1/2) * (1/2) * (1/2) = 1/16 unit
Therefore, after 5 half-lives (i.e. 3000 years in this case), the amount of substance remaining = (1/2)^5 = 1/32 unit.
Hence, the correct answer is option D, i.e. 1/32.
To find: Fraction of sample that would remain after 3000 yr
Solution:
We know that the half-life of a radioactive substance is the time taken for the substance to decay to half of its initial value.
Let the initial amount of the substance be 1 unit.
After 1 half-life, the amount of substance remaining = 1/2 unit
After 2 half-lives, the amount of substance remaining = (1/2) * (1/2) = 1/4 unit
After 3 half-lives, the amount of substance remaining = (1/2) * (1/2) * (1/2) = 1/8 unit
After 4 half-lives, the amount of substance remaining = (1/2) * (1/2) * (1/2) * (1/2) = 1/16 unit
Therefore, after 5 half-lives (i.e. 3000 years in this case), the amount of substance remaining = (1/2)^5 = 1/32 unit.
Hence, the correct answer is option D, i.e. 1/32.
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Community Answer
The half-life of radioactive element is 600 yr. The fraction of sample...
Hey here is the answer put formula n t� = t.
N = 5
R⁰ = 1/ 2⁵
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