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At a certain instant, a piece of radioactive material contains 1012 atoms. The half-life of the material is 0. 693 seconds. Calculate the number of disintegrations in the first second
- a)1012 atoms
- b)106 atoms
- c)1024 atoms
- d)104 atoms
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
At a certain instant, a piece of radioactive material contains 1012ato...
- Now, the radioactive material contains 1012 atoms, hence N0= 1012 atoms
- As, the half-life of the material is 0. 693 seconds, t1/2= 0.693 seconds.
- The value of the disintegration constant will be,
- Thus, the number of disintegration (-dN) in the first second (dt=1) will be,
Hence, the number of disintegrations in the first second is 1012 atoms.
Most Upvoted Answer
At a certain instant, a piece of radioactive material contains 1012ato...
Understanding Radioactive Disintegration
The disintegration of radioactive material can be understood using the half-life concept.
Key Concepts
- Half-Life: The time required for half of the radioactive atoms to decay.
- Disintegration Rate: The number of atoms that decay per unit time.
Given Data
- Initial Number of Atoms: 10^12 atoms
- Half-Life: 0.693 seconds
Calculating Disintegrations in One Second
1. Disintegration Constant (λ):
- The disintegration constant can be calculated using the formula:
λ = 0.693 / Half-Life
Substituting the half-life:
λ = 0.693 / 0.693 = 1 second^-1
2. Disintegration in One Second:
- The number of disintegrations can be calculated by multiplying the initial number of atoms by the disintegration constant:
Disintegrations = N0 * λ
Where N0 is the initial number of atoms:
Disintegrations = 10^12 * 1 = 10^12 disintegrations
Conclusion
- In the first second, the material undergoes 10^12 disintegrations.
- Thus, the correct answer is option 'A'.
This detailed breakdown highlights the relationship between half-life, disintegration constant, and the number of disintegrations in a given time frame.
The disintegration of radioactive material can be understood using the half-life concept.
Key Concepts
- Half-Life: The time required for half of the radioactive atoms to decay.
- Disintegration Rate: The number of atoms that decay per unit time.
Given Data
- Initial Number of Atoms: 10^12 atoms
- Half-Life: 0.693 seconds
Calculating Disintegrations in One Second
1. Disintegration Constant (λ):
- The disintegration constant can be calculated using the formula:
λ = 0.693 / Half-Life
Substituting the half-life:
λ = 0.693 / 0.693 = 1 second^-1
2. Disintegration in One Second:
- The number of disintegrations can be calculated by multiplying the initial number of atoms by the disintegration constant:
Disintegrations = N0 * λ
Where N0 is the initial number of atoms:
Disintegrations = 10^12 * 1 = 10^12 disintegrations
Conclusion
- In the first second, the material undergoes 10^12 disintegrations.
- Thus, the correct answer is option 'A'.
This detailed breakdown highlights the relationship between half-life, disintegration constant, and the number of disintegrations in a given time frame.
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At a certain instant, a piece of radioactive material contains 1012atoms. The half-life of the material is 0. 693 seconds. Calculate the number of disintegrations in the first seconda)1012atomsb)106atomsc)1024 atomsd)104 atomsCorrect answer is option 'A'. Can you explain this answer?
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