Class 12 Exam > Class 12 Questions > At a given time there are 25% undecayed nucle...
Start Learning for Free
At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be about
- a)22 sec
- b)10 sec
- c)12 sec
- d)15 sec
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
At a given time there are 25% undecayed nuclei in a sample. After 10 s...
Half-life of radioactive sample, i.e., the time in which the number of undecayed nuclei becomes half (T) is 10 s.
Mean life, τ=T/loge2=10s/0.693=1.443×10=14.43s ≈ 15s
Mean life, τ=T/loge2=10s/0.693=1.443×10=14.43s ≈ 15s
Most Upvoted Answer
At a given time there are 25% undecayed nuclei in a sample. After 10 s...
Ac to question it can b concludedthat half life is 10 sec, from which rate constant can b calc . As ln2/half time . 1/rate constant is mean life.
Community Answer
At a given time there are 25% undecayed nuclei in a sample. After 10 s...
Given:
- At a given time, there are 25% undecayed nuclei in a sample.
- After 10 seconds, the number of undecayed nuclei reduces to 12.5%.
To find:
The mean life of the nuclei.
Solution:
The decay of radioactive nuclei follows an exponential decay law, which can be expressed as:
N = N0 * e^(-λt)
Where:
- N is the number of undecayed nuclei at time t.
- N0 is the initial number of undecayed nuclei.
- λ is the decay constant.
- t is the time interval.
Step 1:
Let's assume the initial number of undecayed nuclei (N0) is 100 (for easy calculations). Therefore, at the given time, there are 25 undecayed nuclei.
N = 25
N0 = 100
Step 2:
After 10 seconds, the number of undecayed nuclei reduces to 12.5%. This means N = 12.5.
N = N0 * e^(-λt)
12.5 = 100 * e^(-λ * 10)
Step 3:
To find the decay constant (λ), we can rearrange the equation:
e^(-λ * 10) = 12.5 / 100
e^(-λ * 10) = 0.125
Step 4:
Take the natural logarithm (ln) of both sides to solve for λ:
ln(e^(-λ * 10)) = ln(0.125)
-λ * 10 * ln(e) = ln(0.125)
-10λ = ln(0.125)
Step 5:
Solve for λ:
λ = ln(0.125) / -10
Step 6:
Now, we can use the decay constant (λ) to find the mean life of the nuclei (τ):
τ = 1 / λ
τ = 1 / (ln(0.125) / -10)
By calculating the above expression, we get the mean life of the nuclei to be approximately 15 seconds.
Therefore, the correct option is (d) 15 seconds.
- At a given time, there are 25% undecayed nuclei in a sample.
- After 10 seconds, the number of undecayed nuclei reduces to 12.5%.
To find:
The mean life of the nuclei.
Solution:
The decay of radioactive nuclei follows an exponential decay law, which can be expressed as:
N = N0 * e^(-λt)
Where:
- N is the number of undecayed nuclei at time t.
- N0 is the initial number of undecayed nuclei.
- λ is the decay constant.
- t is the time interval.
Step 1:
Let's assume the initial number of undecayed nuclei (N0) is 100 (for easy calculations). Therefore, at the given time, there are 25 undecayed nuclei.
N = 25
N0 = 100
Step 2:
After 10 seconds, the number of undecayed nuclei reduces to 12.5%. This means N = 12.5.
N = N0 * e^(-λt)
12.5 = 100 * e^(-λ * 10)
Step 3:
To find the decay constant (λ), we can rearrange the equation:
e^(-λ * 10) = 12.5 / 100
e^(-λ * 10) = 0.125
Step 4:
Take the natural logarithm (ln) of both sides to solve for λ:
ln(e^(-λ * 10)) = ln(0.125)
-λ * 10 * ln(e) = ln(0.125)
-10λ = ln(0.125)
Step 5:
Solve for λ:
λ = ln(0.125) / -10
Step 6:
Now, we can use the decay constant (λ) to find the mean life of the nuclei (τ):
τ = 1 / λ
τ = 1 / (ln(0.125) / -10)
By calculating the above expression, we get the mean life of the nuclei to be approximately 15 seconds.
Therefore, the correct option is (d) 15 seconds.
|
Explore Courses for Class 12 exam
|
|
Similar Class 12 Doubts
At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer?
Question Description
At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect 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 At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect 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 At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer?.
At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect 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 At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect 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 At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer?.
Solutions for At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice At a given time there are 25% undecayed nuclei in a sample. After 10 seconds number of undecayed nuclei reduces to 12.5%. Then mean life of the nuclei will be abouta)22 secb)10 secc)12 secd)15 secCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 12 tests.
|
|
Explore Courses for Class 12 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup