Earth's Quantized Angular Momentum and Energy Transition in the Bohr Model?

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Homework Help Overview

The discussion revolves around the concept of quantized angular momentum in the context of Earth's motion around the sun, drawing parallels to the Bohr model of the hydrogen atom. The original poster poses a series of questions regarding the quantum number of Earth, energy transitions, and the implications of these transitions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of the quantum number using Earth's physical characteristics and question the appropriateness of parameters used in energy calculations. There is uncertainty regarding the value of z in the energy equation and the validity of the resulting energy value.

Discussion Status

Some participants have provided guidance on calculating the quantum number and suggested methods for determining energy differences between quantum states. Multiple interpretations of the problem are being explored, particularly regarding the energy calculations and the parameters involved.

Contextual Notes

There is a lack of clarity on the appropriate values for certain variables, such as z in the energy equation, and the original poster expresses confusion about how to approach the problem. The discussion is framed within the constraints of a homework assignment, which may limit the exploration of certain concepts.

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Homework Statement



4-16:
if the angular momentum of the Earth in its motion around the sun were quantized like a hydrogen electron according to equation L=mvr=(nh)/2Π, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? would that energy release (presumably as a gravity wave) be detectable? what would be the radius of that orbit? (radius of Earth's orbit is 1.5x10^11 m

Homework Equations





The Attempt at a Solution


don't even know where to start! :(
 
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Try finding out what n is using the physical characteristics of the Earth.
 
ok so i set nh/2pi equal to L which is 7.27e-5 rad/s and i solved for n. I got 6.2e29.
for the next part with the energy, i have this equation: [m(k^2)(z^2)(e^2)]/[(2h^2)(n^2)]
but i don't know what i would use for z. when i use z=1 i get that E= 7.7e-40 J but that just seems very wrong.
 
I believe we need to find out how much energy it would take to go from n to n-1. So find the energy at E(n) and subtract E(n-1). See if that gives you something more reasonable.
 

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