 GR 8677927796770177 | # Login | Register

GR0177 #31
Problem
 GREPhysics.NET Official Solution Alternate Solutions
This problem is still being typed.
Atomic}Positronium

The positronium atom ground-state energy can be deduced from recalling the reduced mass. , since one has a positron and electron orbiting each other, and thus the energy, which is related to mass, is half of that of Hydrogen.

The Bohr formula still applies, and thus , which is choice (A).  Alternate Solutions
 FutureDrSteve2011-11-07 12:22:35 Oops, this was supposed to be a separate post, not a reply.... If you realize that the ground state energy of positronium is roughly -6.8eV (which I think you have to in order to solve this problem), you don't have to do any math. An electron transitioning down from n= would have initial potential energy of 0, and drop down to final energy -6.8eV, for a max energy change of 6.8eV, eliminating (C), (D), and (E). Since the electron is only falling down from n=3, it stands to reason that the photon would be less energetic than 6.8eV, leaving only answer (A).Reply to this comment bill92
2014-10-27 13:17:41
I just took the exam and there was no positronium question! All my studying was for naught!

Just kidding, I think it went well. Thanks to Yosun for this very helpful site! FutureDrSteve
2011-11-07 12:22:35
Oops, this was supposed to be a separate post, not a reply....

If you realize that the ground state energy of positronium is roughly -6.8eV (which I think you have to in order to solve this problem), you don't have to do any math. An electron transitioning down from n= would have initial potential energy of 0, and drop down to final energy -6.8eV, for a max energy change of 6.8eV, eliminating (C), (D), and (E). Since the electron is only falling down from n=3, it stands to reason that the photon would be less energetic than 6.8eV, leaving only answer (A). Tommy Koulax
2007-10-31 17:48:57
Why is the reduced mass m/2 ?
 nick12342007-11-02 17:16:11 For the hydrogen atom, dominates the denominator, and becomes For positronium, , so rinnie
2007-03-26 21:27:49
Hydrogen levels E3 - E1 = -1.5 + 13.6 = 12.1/2 = 6.05.
Energy level of positronium is half those of Hydrogen.
 FutureDrSteve2011-11-07 12:20:53 If you realize that the ground state energy of positronium is roughly -6.8eV (which I think you have to in order to solve this problem), you don't have to do any math. An electron transitioning down from n= would have initial potential energy of 0, and drop down to final energy -6.8eV, for a max energy change of 6.8eV, eliminating (C), (D), and (E). Since the electron is only falling down from n=3, it stands to reason that the photon would be less energetic than 6.8eV, leaving only answer (A). You are replying to:
Why is the reduced mass m/2 ?     LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces . type this... to get...$\int_0^\infty\partial\Rightarrow\ddot{x},\dot{x}\sqrt{z}\langle my \rangle\left( abacadabra \right)_{me}\vec{E}\frac{a}{b}\$