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If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain?
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If Zera finds a rock in the forbidden zane that is tainted with pluton...
Answer:
The activity of a radioactive sample is defined as the number of decays per second. It is related to the number of radioactive atoms in the sample by the following equation:
A = λN
where A is the activity, λ is the decay constant, and N is the number of radioactive atoms.
We can rearrange this equation to solve for the number of radioactive atoms:
N = A/λ
The decay constant is related to the half-life by the following equation:
λ = ln(2)/t1/2
Substituting the given values, we get:
λ = ln(2)/24,900 = 2.784 x 10-5 yr-1
N = A/λ = 100 Bq / 2.784 x 10-5 yr-1 = 3.59 x 106 radioactive atoms
Therefore, the rock contains 3.59 x 106 plutonium-239 atoms when discovered.
The number of radioactive atoms in a sample decreases exponentially with time according to the following equation:
N(t) = N0 e-λt
where N(t) is the number of radioactive atoms at time t, N0 is the initial number of radioactive atoms, and e is the base of the natural logarithm.
Substituting the given values, we get:
N(t) = N0 e-λt = 3.59 x 106 e-2.784 x 10-5 x 500 = 3.63 x 106 radioactive atoms
Therefore, the rock originally contained 3.63 x 106 plutonium-239 atoms.
Given:
- Activity (A) of plutonium-239 in the rock = 100 Bq
- Half-life (t1/2) of plutonium-239 = 24,900 years
- Time elapsed (t) between explosion and discovery = 500 years
To Find:
- Number of plutonium-239 atoms in the rock when discovered
- Number of plutonium-239 atoms in the rock originally
Solution:
Number of Plutonium-239 Atoms in the Rock When Discovered:
The activity of a radioactive sample is defined as the number of decays per second. It is related to the number of radioactive atoms in the sample by the following equation:
A = λN
where A is the activity, λ is the decay constant, and N is the number of radioactive atoms.
We can rearrange this equation to solve for the number of radioactive atoms:
N = A/λ
The decay constant is related to the half-life by the following equation:
λ = ln(2)/t1/2
Substituting the given values, we get:
λ = ln(2)/24,900 = 2.784 x 10-5 yr-1
N = A/λ = 100 Bq / 2.784 x 10-5 yr-1 = 3.59 x 106 radioactive atoms
Therefore, the rock contains 3.59 x 106 plutonium-239 atoms when discovered.
Number of Plutonium-239 Atoms in the Rock Originally:
The number of radioactive atoms in a sample decreases exponentially with time according to the following equation:
N(t) = N0 e-λt
where N(t) is the number of radioactive atoms at time t, N0 is the initial number of radioactive atoms, and e is the base of the natural logarithm.
Substituting the given values, we get:
N(t) = N0 e-λt = 3.59 x 106 e-2.784 x 10-5 x 500 = 3.63 x 106 radioactive atoms
Therefore, the rock originally contained 3.63 x 106 plutonium-239 atoms.
Conclusion:
- The rock contains 3.59 x 106 plutonium-239 atoms when discovered.
- The rock originally contained 3.63 x 106 plutonium-239 atoms.
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If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain?
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If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain?.
If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain?.
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If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain?, a detailed solution for If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? has been provided alongside types of If Zera finds a rock in the forbidden zane 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) Exercise 15, if the explosion occurred 500. y prior to Zera's discovery, how many plutonium-239 atoms did the rock originally contain? theory, EduRev gives you an
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