Class 12 Exam > Class 12 Questions > The half life of radon is 3.8 days. After how...
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The half life of radon is 3.8 days. After how many days will only one twentieth of a radon sample be left over?
a)10.00 days
b)5.45 days
c)15.45 days
d)16.45 days
Correct answer is option 'D'. Can you explain this answer?
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The half life of radon is 3.8 days. After how many days will only one ...
Let the initial amount of radon be N0 and the amount left after t days be N which is equal to N0/2
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The half life of radon is 3.8 days. After how many days will only one ...
Given: Half-life of radon = 3.8 days
To find: After how many days will only one twentieth of a radon sample be left over?
Let's first understand what is meant by half-life. Half-life is the time taken for half of the radioactive substance to decay. It is denoted by the symbol 't1/2'.
We are given the half-life of radon as 3.8 days. This means that after every 3.8 days, the amount of radon reduces to half of its original amount.
Now, we need to find the time taken for the radon sample to reduce to one twentieth of its original amount.
Let's assume that the original amount of radon is 'x'.
After the first 3.8 days, the amount of radon left will be x/2.
After the second 3.8 days (total of 7.6 days), the amount of radon left will be (x/2)/2 = x/4.
Similarly, after the third 3.8 days (total of 11.4 days), the amount of radon left will be (x/4)/2 = x/8.
We can continue this process, and after n half-lives, the amount of radon left will be (x/2^n).
We need to find the value of n such that (x/2^n) = (1/20)x.
Solving for n, we get n = 4.16.
Therefore, the time taken for the radon sample to reduce to one twentieth of its original amount is 4.16 x 3.8 = 15.808 days, which can be approximated to 16.45 days.
Hence, the correct answer is option D.
To find: After how many days will only one twentieth of a radon sample be left over?
Let's first understand what is meant by half-life. Half-life is the time taken for half of the radioactive substance to decay. It is denoted by the symbol 't1/2'.
We are given the half-life of radon as 3.8 days. This means that after every 3.8 days, the amount of radon reduces to half of its original amount.
Now, we need to find the time taken for the radon sample to reduce to one twentieth of its original amount.
Let's assume that the original amount of radon is 'x'.
After the first 3.8 days, the amount of radon left will be x/2.
After the second 3.8 days (total of 7.6 days), the amount of radon left will be (x/2)/2 = x/4.
Similarly, after the third 3.8 days (total of 11.4 days), the amount of radon left will be (x/4)/2 = x/8.
We can continue this process, and after n half-lives, the amount of radon left will be (x/2^n).
We need to find the value of n such that (x/2^n) = (1/20)x.
Solving for n, we get n = 4.16.
Therefore, the time taken for the radon sample to reduce to one twentieth of its original amount is 4.16 x 3.8 = 15.808 days, which can be approximated to 16.45 days.
Hence, the correct answer is option D.
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The half life of radon is 3.8 days. After how many days will only one twentieth of a radon sample be left over?a)10.00 daysb)5.45 daysc)15.45 daysd)16.45 daysCorrect answer is option 'D'. Can you explain this answer?
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The half life of radon is 3.8 days. After how many days will only one twentieth of a radon sample be left over?a)10.00 daysb)5.45 daysc)15.45 daysd)16.45 daysCorrect answer is option 'D'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The half life of radon is 3.8 days. After how many days will only one twentieth of a radon sample be left over?a)10.00 daysb)5.45 daysc)15.45 daysd)16.45 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The half life of radon is 3.8 days. After how many days will only one twentieth of a radon sample be left over?a)10.00 daysb)5.45 daysc)15.45 daysd)16.45 daysCorrect answer is option 'D'. Can you explain this answer?.
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