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In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)?
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Calculation of Plutonium Atoms in the Rock from Activity
The activity of the rock is given as 100. Bq. The activity of a radioactive substance is defined as the number of decay events per second. Plutonium-239 is a radioactive isotope that undergoes decay through alpha emission. The decay constant (λ) of the isotope is given by the half-life (t1/2) as follows:
λ = ln(2) / t1/2
For Plutonium-239, we have:
λ = ln(2) / 24,900 yrs
λ = 2.78 × 10^-5 per year
The activity (A) of the rock is related to the number of atoms (N) of Plutonium-239 by the following equation:
A = λN
Rearranging the equation, we get:
N = A / λ
Substituting the given values, we get:
N = 100 Bq / (2.78 × 10^-5 per year)
N = 3.60 × 10^6 atoms
Therefore, the rock contains 3.60 × 10^6 atoms of Plutonium-239 when it is discovered in the forbidden zone.
Explanation
Plutonium-239 is a radioactive isotope that undergoes decay through alpha emission. The decay constant of the isotope is related to its half-life. The activity of a radioactive substance is defined as the number of decay events per second. The activity of the rock is given in Bq, which is equivalent to decay events per second. The number of atoms of Plutonium-239 in the rock can be calculated using the activity and the decay constant of the isotope.
The activity of the rock is given as 100. Bq. The activity of a radioactive substance is defined as the number of decay events per second. Plutonium-239 is a radioactive isotope that undergoes decay through alpha emission. The decay constant (λ) of the isotope is given by the half-life (t1/2) as follows:
λ = ln(2) / t1/2
For Plutonium-239, we have:
λ = ln(2) / 24,900 yrs
λ = 2.78 × 10^-5 per year
The activity (A) of the rock is related to the number of atoms (N) of Plutonium-239 by the following equation:
A = λN
Rearranging the equation, we get:
N = A / λ
Substituting the given values, we get:
N = 100 Bq / (2.78 × 10^-5 per year)
N = 3.60 × 10^6 atoms
Therefore, the rock contains 3.60 × 10^6 atoms of Plutonium-239 when it is discovered in the forbidden zone.
Explanation
Plutonium-239 is a radioactive isotope that undergoes decay through alpha emission. The decay constant of the isotope is related to its half-life. The activity of a radioactive substance is defined as the number of decay events per second. The activity of the rock is given in Bq, which is equivalent to decay events per second. The number of atoms of Plutonium-239 in the rock can be calculated using the activity and the decay constant of the isotope.
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In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)?
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In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)?.
In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered? (Half-life of plutonium-239 is 24 900. y)?.
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