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If a radioactive material is decayed by 29.28% in 10 minute, then its half life will be:-
Correct answer is '20'. Can you explain this answer?
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If a radioactive material is decayed by 29.28% in 10 minute, then its ...
Given: A radioactive material is decayed by 29.28% in 10 minutes.
To find: Half-life of the radioactive material.
Solution:
Let's assume the initial quantity of the radioactive material to be 'N0'.
After 10 minutes, the quantity of the material remaining will be 70.72% of N0 (as it has decayed by 29.28%).
Therefore, the quantity of material remaining after 10 minutes = 0.7072*N0.
Let's assume the half-life of the material to be 't1/2'.
The formula for half-life is given by:
N(t) = N0*(1/2)^(t/t1/2)
where, N(t) is the quantity of material remaining after time 't'.
Substituting t = 10 minutes and N(t) = 0.7072*N0, we get:
0.7072*N0 = N0*(1/2)^(10/t1/2)
Simplifying the above equation, we get:
1/2^(10/t1/2) = 0.7072
Taking the logarithm of both sides, we get:
log(1/2^(10/t1/2)) = log(0.7072)
(-10/t1/2)*log(2) = log(0.7072)
(-10/t1/2) = log(0.7072) / log(2)
t1/2 = -10 / (log(0.7072) / log(2))
t1/2 = 20.03 minutes (approx.)
Therefore, the half-life of the radioactive material is approximately 20 minutes.
To find: Half-life of the radioactive material.
Solution:
Let's assume the initial quantity of the radioactive material to be 'N0'.
After 10 minutes, the quantity of the material remaining will be 70.72% of N0 (as it has decayed by 29.28%).
Therefore, the quantity of material remaining after 10 minutes = 0.7072*N0.
Let's assume the half-life of the material to be 't1/2'.
The formula for half-life is given by:
N(t) = N0*(1/2)^(t/t1/2)
where, N(t) is the quantity of material remaining after time 't'.
Substituting t = 10 minutes and N(t) = 0.7072*N0, we get:
0.7072*N0 = N0*(1/2)^(10/t1/2)
Simplifying the above equation, we get:
1/2^(10/t1/2) = 0.7072
Taking the logarithm of both sides, we get:
log(1/2^(10/t1/2)) = log(0.7072)
(-10/t1/2)*log(2) = log(0.7072)
(-10/t1/2) = log(0.7072) / log(2)
t1/2 = -10 / (log(0.7072) / log(2))
t1/2 = 20.03 minutes (approx.)
Therefore, the half-life of the radioactive material is approximately 20 minutes.
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If a radioactive material is decayed by 29.28% in 10 minute, then its half life will be:-Correct answer is '20'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a radioactive material is decayed by 29.28% in 10 minute, then its half life will be:-Correct answer is '20'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a radioactive material is decayed by 29.28% in 10 minute, then its half life will be:-Correct answer is '20'. Can you explain this answer?.
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