lekh2003
Gold Member
 506
 264
1. The problem statement, all variables and given/known data
2. Relevant equations
I've used:
##mv^2/r## = Centripetal
##q^2/r^2## = Force pulling the electron in
A bunch of other ones which I really can't be bothered listing.
3. The attempt at a solution
I managed to get Part A of the question using pretty simple methods.
I set ##mv^2/r = q^2/r^2##
That gave me ##v = sqrt(q^2/mr)##
And I plugged that into the equation for KE and got ##q^2/2r##
Then I need to transform the change in energy to the energy lost per orbital, so I used the time it takes to take each orbit using some orbital formula: ##t=2πr/v##
Keep going, and keep going, and eventually I found an equation for the change in energy due to radiation of energy, which I compared as a ratio to the kinetic energy, and it was basically negligible as an effect.
But Part B is beating me up. I really don't understand what to do. I was suspicious I must find a correlation between the energy and the radius, so I checked the solution and I got this:
However, I simply don't understand how they seemed to get these magical values.
After this, its some differential equations which I might have trouble understanding later, but right now I dont understand this step and what they're doing.
Thanks.
2. Relevant equations
I've used:
##mv^2/r## = Centripetal
##q^2/r^2## = Force pulling the electron in
A bunch of other ones which I really can't be bothered listing.
3. The attempt at a solution
I managed to get Part A of the question using pretty simple methods.
I set ##mv^2/r = q^2/r^2##
That gave me ##v = sqrt(q^2/mr)##
And I plugged that into the equation for KE and got ##q^2/2r##
Then I need to transform the change in energy to the energy lost per orbital, so I used the time it takes to take each orbit using some orbital formula: ##t=2πr/v##
Keep going, and keep going, and eventually I found an equation for the change in energy due to radiation of energy, which I compared as a ratio to the kinetic energy, and it was basically negligible as an effect.
But Part B is beating me up. I really don't understand what to do. I was suspicious I must find a correlation between the energy and the radius, so I checked the solution and I got this:
However, I simply don't understand how they seemed to get these magical values.
After this, its some differential equations which I might have trouble understanding later, but right now I dont understand this step and what they're doing.
Thanks.
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