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A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance is
- a)2.5 days
- b)5 days
- c)10 days
- d)20 days
Correct answer is option 'C'. Can you explain this answer?
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A radioactive substance decays to 1/16th of its initial activity in 40...
**Given:**
- A radioactive substance decays to 1/16th of its initial activity in 40 days.
**To find:**
- The half-life of the radioactive substance.
**Explanation:**
The half-life of a radioactive substance is the time taken for the substance to decay to half of its initial activity.
Let's assume the initial activity of the substance is A0.
After one half-life, the activity of the substance will be A0/2.
After two half-lives, the activity of the substance will be (A0/2)/2 = A0/4.
After three half-lives, the activity of the substance will be ((A0/2)/2)/2 = A0/8.
After four half-lives, the activity of the substance will be (((A0/2)/2)/2)/2 = A0/16.
In the given question, it is mentioned that the substance decays to 1/16th of its initial activity in 40 days. This means that it takes four half-lives for the substance to decay to 1/16th of its initial activity.
Therefore, the half-life of the substance can be calculated by dividing the given time (40 days) by the number of half-lives (4).
Half-life = 40 days / 4 = 10 days.
Hence, the correct answer is option C) 10 days.
- A radioactive substance decays to 1/16th of its initial activity in 40 days.
**To find:**
- The half-life of the radioactive substance.
**Explanation:**
The half-life of a radioactive substance is the time taken for the substance to decay to half of its initial activity.
Let's assume the initial activity of the substance is A0.
After one half-life, the activity of the substance will be A0/2.
After two half-lives, the activity of the substance will be (A0/2)/2 = A0/4.
After three half-lives, the activity of the substance will be ((A0/2)/2)/2 = A0/8.
After four half-lives, the activity of the substance will be (((A0/2)/2)/2)/2 = A0/16.
In the given question, it is mentioned that the substance decays to 1/16th of its initial activity in 40 days. This means that it takes four half-lives for the substance to decay to 1/16th of its initial activity.
Therefore, the half-life of the substance can be calculated by dividing the given time (40 days) by the number of half-lives (4).
Half-life = 40 days / 4 = 10 days.
Hence, the correct answer is option C) 10 days.
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A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance isa)2.5 daysb)5 daysc)10 daysd)20 daysCorrect answer is option 'C'. Can you explain this answer?
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