Solution Found!
Show that the time required for an electron in the nth
Chapter 31, Problem 87GP(choose chapter or problem)
Show the time required for an electron in the \(n\)th Bohr orbit of hydrogen to circle the nucleus once is given by \(T=T_{1} n^{3} \quad n=1,2,3, \ldots\) where \(T_{1}=h^{3} / 4 \pi^{2} m k^{2} e^{4}\)
Equation Transcription:
Text Transcription:
n
T = T_{1} n^{3} n = 1,2,3, …
T_1 = h^{3} / 4pi^{2} mk^{2} e^{4}
Questions & Answers
QUESTION:
Show the time required for an electron in the \(n\)th Bohr orbit of hydrogen to circle the nucleus once is given by \(T=T_{1} n^{3} \quad n=1,2,3, \ldots\) where \(T_{1}=h^{3} / 4 \pi^{2} m k^{2} e^{4}\)
Equation Transcription:
Text Transcription:
n
T = T_{1} n^{3} n = 1,2,3, …
T_1 = h^{3} / 4pi^{2} mk^{2} e^{4}
ANSWER:
Solution 87GP
Step 1 of 2
The equation for the time period,
Where, - Distance travelled
- Speed of the motion
Since the orbit is circular, we can write,
Where - Radius of the nth orbit
Therefore,
We know that,
Where, - State of the atom
- Planck’s constant
- mass of the electron
- Charge of the electron
