Concept explainers
The time taken by the electron of the hydrogen atom to
Answer to Problem 18P
The time taken by the electron of the hydrogen atom to radiate its energy and crash into the nucleus is
Explanation of Solution
Write the expression for
Here,
Differentiate above equation with respect to time.
Write the expression for radiated Power in electromagnetic theory.
Here,
Power radiated is equal to Energy radiated per unit time.
Compare equation (I) with equation (II).
Simplify above equation.
In a circular orbit, centripetal acceleration is given by:
Write the expression for centripetal acceleration.
Here,
Write the expression for force.
Here,
Substitute
Substitute
Rearrange above equation.
Integrate above equation.
Conclusion:
Substitute
Thus, the time taken by the electron of the hydrogen atom to radiate its energy and crash into the nucleus is
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