Concept explainers
(a)
To show: The nucleus carries away a fraction
(a)
Answer to Problem 65GP
The nucleus carries away a fraction
Explanation of Solution
Given:
Alpha decay of a
Formula used:
Kinetic energy can be given as:
Calculation:
Now, using the law of conservation of momentum, it can be concluded that the momentum of the daughter nucleus will be equal to the momentum of alpha particle as follows:
So, the kinetic energy of the daughter nucleus will be given as:
Using equation (1), we get:
Now, the momentum of the alpha particle can be written as:
So, the previous equation becomes:
Here,
Conclusion:
Hence, the ratio is equal to
(b)
To find: The percentage of the energy available.
(b)
Answer to Problem 65GP
The percentage carried away by the alpha particle is given by is 98.23%
Explanation of Solution
Given:
Alpha decay of a
Calculation:
The decay equation can be written as:
So, the mass number of the daughter nucleus is
Using
Hence, the percentage carried away by the alpha particle is given by:
Conclusion:
Hence, the percentage carried away by the alpha particle is given by is 98.23%
Chapter 30 Solutions
Physics: Principles with Applications
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