What is the Orbit of Hydrogen Atom for an Electron at 734 km/s?

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Homework Help Overview

The discussion revolves around determining the orbit of a hydrogen atom's electron given its speed of 734 km/s. The context is rooted in atomic physics, specifically the Bohr model of the hydrogen atom.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply Bohr's second postulate to find the radius of the electron's orbit. Some participants question the validity of the radius derived from the initial assumptions and suggest the need for additional equations to relate radius to quantum number or velocity.

Discussion Status

The discussion is ongoing, with participants exploring different equations that could relate the radius of the orbit to the quantum number or the speed of the electron. There is no explicit consensus yet, but guidance has been offered regarding the use of force balance equations.

Contextual Notes

Participants note that the radius value derived corresponds to the first Bohr orbit, raising questions about the implications for higher quantum numbers and the need for further information or equations to resolve the problem.

gruba
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Homework Statement


On which orbit of hydrogen atom an electron has the speed of 734 km/s?

Homework Equations


Bohr's second postulate: mvr=nh,m=9.109\cdot 10^{-31}kg,v=734 km/s,h=6.626\cdot 10^{-34} m^{2}kg/s

The Attempt at a Solution


By using the second Bohr's postulate, we get 6686.006\cdot 10^{-28}r=6.626\cdot 10^{-34}n

Question: What is the value of radius of orbit of electron, r?

If we set that r=0.0529 nm, then we get n=0.053 and n should be positive integer.
 
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gruba said:
If we set that r=0.0529 nm
That value is for the first Bohr orbit, ##n=1##. For ##n > 1##, the radius is bigger. You need another equation relating ##r## to ##n## or ##r## to ##v##.
 
DrClaude said:
That value is for the first Bohr orbit, ##n=1##. For ##n > 1##, the radius is bigger. You need another equation relating ##r## to ##n## or ##r## to ##v##.

What is that equation?
 
You can use the equation that balances the centripetal force and the Coulomb force. Don't you have that equation in your notes/textbook?
 

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