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.

wittensdog
2009-07-28 11:02:09

Everyone I have ever talked to who has taken the physics GRE has said there was a positronium question on their test.

I'm glad ETS gets to dictate what's important in physics. Apparently it's positronium. Yes. Positronium is the most important thing in physics. Ever.

I understand knowing how to use reduced mass is important, but still, it seems a little over the top to me.

jcsoldier11
2009-10-26 00:16:10

According to my friend who took it a couple weeks ago, there was a Positronium question on it in which he did basically the same thing as above.

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 ?

; )

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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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$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
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$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

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