GREPhysics.NET: GR8677 #99

GR8677 #99

Problem

GREPhysics.NET Official Solution

Atomic $\Rightarrow$ }Positronium

Interestingly, this is almost an exact repeat of Exam 9677 Prob 12. The reasoning's the same:

The positronium atom involves a positron-electron combination instead of the usual proton-electron combo for the H atom. Charge remains the same, and thus one can approximate its eigenvalue by changing the mass of the Rydberg energy (recall that the ground state of the Hydrogen atom is 1 Rydberg).

Recall the reduced mass $\mu=\frac{m_1 m_2}{m_1+m_2}$ , where for identical masses, one obtains $\mu = m/2$ . The Rydberg in the regular Hydrogen energy eigenvalue formula $E=R\left(1/n_f^2 - 1/n_i^2 \right)$ is $R\propto \mu$ , where $\mu \rightarrow \mu/2$ . Substitute in the new value of the reduced mass to get $E\approx R/2$ . $R=-13.6$ eV, and thus $E\approx -6.8$ eV.

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Comments

Richard 2007-11-01 13:56:01	I think there is a positronium question akin to this one on all of the released phyiscs GRE's. Hint I think. Reply to this comment
Blake7 2007-09-26 01:23:16	Yosun, Don't you mean that 9677.12 is almost an exact repeat of 8677.99 ? ; ) Reply to this comment

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I think there is a positronium question akin to this one on all of the released phyiscs GRE's. Hint I think.

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LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

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