Concept explainers
(a)
The energy released during the beta decay.
(a)
Answer to Problem 33P
The energy released during the beta decay is
Explanation of Solution
Write the given reaction of beta decay
Here,
Write the expression for energy released in this reaction
Here,
Conclusion:
Substitute
Therefore, the energy released during the beta decay is
(b)
The speed of the proton and the electron.
(b)
Answer to Problem 33P
The speed of the proton and electron is
Explanation of Solution
Write the expression for conservation of momentum
Here,
The neutron is initially at rest and hence the momentum of the neutron in zero.
Rewrite equation (III)
Write the expression for conservation of energy
Rewrite the above expression using (IV)
Write the expression for the relativistic momentum of the proton
Here,
Rewrite the above expression
Similarly write the expression for speed of the electron
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the speed of the proton and electron is
(c)
The particle moving at relativistic speed.
(c)
Answer to Problem 33P
Electron is moving at relativistic speed.
Explanation of Solution
If the speed of the particle is comparable to that of the
Conclusion:
From part (b), the speed of the proton and electron is
Therefore, electron is moving at relativistic speed.
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Chapter 15 Solutions
Modern Physics
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