Concept explainers
(a)
Show that the electron in classical hydrogen atom spirals into nucleus at a rate
(a)
Answer to Problem 4P
The electron in classical hydrogen atom spirals into nucleus at a rate
Explanation of Solution
Write the equation for acceleration according to Newton’s second law.
Here,
Write the equation for the force experienced by the particle moving in a uniform circular motion.
Here,
Write the acceleration equation using the above equation and substitute
Here,
Write the equation for centripetal acceleration.
Here,
Compare equations (III) and (IV) and rearrange to find
Write the equation for the total energy.
Here,
Write the equation for kinetic energy.
Write the equation for potential energy.
Substitute the equation (VII) and (VIII) in equation (VI) and use equation (V) to find E.
Conclusion:
Write the time given time derivative equation for energy.
Substitute the equation (III) and (IX) in the above equation.
Thus, the electron in classical hydrogen atom spirals into nucleus at a rate
(b)
The time interval over which the electron reaches
(b)
Answer to Problem 4P
The time interval over which the electron reaches
Explanation of Solution
Write the equation for the rate at which the electron in classical hydrogen atom spirals into nucleus.
Take the integral of the time.
Here,
Substitute equation (X) in (XI) to find
Conclusion:
Substitute
Thus, the time interval over which the electron reaches
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Chapter 41 Solutions
Physics for Scientists and Engineers with Modern Physics
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