JEE Exam > JEE Questions > The radionuclide56Mnis being produced in a cy...
Start Learning for Free
The radionuclide 56Mn is being produced in a cyclotron at a constant rate P by bombarding a manganese target with deutrons. 56Mn has a half life of 2.5 hours and the target contains large number of only the stable manganese isotope 55Mn. The reaction that produces 56Mn is:
55Mn + d →56Mn+P
After being bombarded for a long time, the activity of 56Mn becomes constant equal to 13.86×1010s−1. (Use ln2 = 0.693; Avogadro number = 6×1023; atomic weight of 56Mn = 56gm/mole)
Q. After a long time bombardment, number of 56Mn nuclei present in the target depends upon
(a) The number of 56Mn nuclei present at the start of the process
(b) Half life of the 56Mn
(c) The constant rate of production P
(a) The number of 56Mn nuclei present at the start of the process
(b) Half life of the 56Mn
(c) The constant rate of production P
- a)All (a), (b) and (c) are correct
- b)Only (a) and (b) are correct
- c)Only (b) and (c) are correct
- d)Only (a) and (c) are correct
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The radionuclide56Mnis being produced in a cyclotron at a constant rat...
The number of 56Mn nuclei present in the target after a long time bombardment depends on the constant rate of production P and the half life of the 56Mn.
The half life of a radioisotope is the time it takes for the activity of the radioisotope to decrease by half. After a long time bombardment, the activity of 56Mn becomes constant, meaning that the rate at which 56Mn nuclei are being produced is equal to the rate at which they are decaying. This means that the number of 56Mn nuclei present in the target is not changing.
Therefore, the number of 56Mn nuclei present in the target depends on the constant rate of production P and the half life of the 56Mn. The number of 56Mn nuclei present at the start of the process does not affect the number of 56Mn nuclei present in the target after a long time bombardment.
The correct answer is therefore (c) Only (b) and (c) are correct.
Free Test
FREE
| Start Free Test |
Community Answer
The radionuclide56Mnis being produced in a cyclotron at a constant rat...
→ 56Mn + n
Given that the rate of production of 56Mn is constant at P, we can write the differential equation for the rate of change of 56Mn concentration as:
d[56Mn]/dt = P
Since 56Mn has a half-life of 2.5 hours, we can relate the rate of change of 56Mn concentration to its decay constant λ:
λ = ln(2) / (2.5 hours)
The decay constant can also be related to the rate of change of 56Mn concentration through the equation:
d[56Mn]/dt = -λ[56Mn]
Equating the two expressions for the rate of change of 56Mn concentration, we have:
P = -λ[56Mn]
Simplifying, we have:
[56Mn] = -P/λ
Therefore, the concentration of 56Mn can be determined by dividing the production rate P by the decay constant λ.
Given that the rate of production of 56Mn is constant at P, we can write the differential equation for the rate of change of 56Mn concentration as:
d[56Mn]/dt = P
Since 56Mn has a half-life of 2.5 hours, we can relate the rate of change of 56Mn concentration to its decay constant λ:
λ = ln(2) / (2.5 hours)
The decay constant can also be related to the rate of change of 56Mn concentration through the equation:
d[56Mn]/dt = -λ[56Mn]
Equating the two expressions for the rate of change of 56Mn concentration, we have:
P = -λ[56Mn]
Simplifying, we have:
[56Mn] = -P/λ
Therefore, the concentration of 56Mn can be determined by dividing the production rate P by the decay constant λ.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer?
Question Description
The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. 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 The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer?.
The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. 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 The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The radionuclide56Mnis being produced in a cyclotron at a constant ratePby bombarding a manganese target with deutrons.56Mnhas a half life of 2.5 hours and the target contains large number of only the stable manganese isotope55Mn. The reaction that produces56Mnis:55Mn + d→56Mn+PAfter being bombarded for a long time, the activity of56Mnbecomes constant equal to13.86×1010s−1. (Useln2 = 0.693; Avogadro number =6×1023; atomic weight of56Mn= 56gm/mole)Q. After a long time bombardment, number of56Mn nuclei present in the target depends upon(a) The number of56Mnnuclei present at the start of the process(b) Half life of the56Mn(c) The constant rate of productionPa)All (a), (b) and (c) are correctb)Only (a) and (b) are correctc)Only (b) and (c) are correctd)Only (a) and (c) are correctCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup