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  GR8677 #99
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Verbatim question for GR8677 #99
Atomic}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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azwar33
2016-03-12 23:07:47		Lowongan Kerja Cara " target="_blank">http://pastihamil.blogspot.co.id/\">Cara Cepat Hamil \\NEC
Geez
2015-10-22 23:02:29		It\\\\\\\'s 13.6 ev with ~infinitely massive proton -> no proton KE. If positron can move, it will share same pool of energy with electron. The coulomb potential is the same as for hydrogen because the charges are the same as with hydrogen, so they each get (1/2) the total energy since they are same mass. -> (1/2)13.6 eV = answer B, as given in booklet.
azwar33
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NEC
cz
2012-11-04 22:22:31		Not really a great way of doing problems. Your method will give the answer here. The reason that happens is because in the actual formula for the ground state energy is proportional to m\cdote^4\cdotZ^2
Here m is the reduced mass of the electron.

For the hydrogen atom it is just the same as electron mass (since the nucleus is so heavy).
For the positronium it is half of original mass, since the positron has the same mass as the electron.		NEC
TheDoctor
2012-08-22 12:22:17		Could you say that you know energy is proportional to mass (rest energy = m*c^2), thus it is proportional to reduced mass, and then make the reduced mass argument that you made about \mu going to \mu/2}?
cz
2012-11-04 22:25:23		 Not really a great way of doing problems. Your method will give the answer here. The reason that happens is because in the actual formula for the ground state, energy is given by m_ee^4Z^2
Here m is the reduced mass.

For the hydrogen atom m is almost the same as the electron mass. (the nucleus is 1840 times heavier)

For positronium, m is half of the electron mass. (positronium is the same mass as the electron).

If in the formula m^2 or anything else like that appeared, then your line of argument would always fail.
cz
2012-11-04 22:26:26		 Actually energy is just proportional to what I have posted. I left out the constants.
Answered Question!
anum
2010-11-11 12:30:34		what i did was E directly proportional to m .m halved then energy halved.( by E i mean the ground state energy of hydrogen of which formula i have memorized)NEC
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.
mvgnzls
2011-09-14 19:00:13		 postironium is important coming from a person working in the positron lab at UCR!!!
NEC
Blake7
2007-09-26 01:23:16		Yosun,

Don't you mean that 9677.12 is almost an exact repeat of 8677.99 ?

; )
NEC

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http://bit.ly/1NPu46B http://bit.ly/1mcuCNC\r\nhttp://bit.ly/1TCO5EA http://bit.ly/20pl2tG http://bit.ly/1QFRhN6 http://bit.ly/1Pz9Aog\r\nhttp://bit.ly/1Pglrny http://bit.ly/1mcuQnO http://bit.ly/1o5mkZp http://bit.ly/1Kpxouq\r\nhttp://bit.ly/1Kpxq5u http://bit.ly/1R1fFuD http://bit.ly/1X2HdjU http://bit.ly/1Pz9MUw\r\nhttp://bit.ly/1NPunOU http://bit.ly/1X2HjYQ http://bit.ly/1PglK1Q http://bit.ly/1R1fNdF\r\nhttp://bit.ly/1NPutpI http://bit.ly/20plzvq http://bit.ly/1nGaHHT http://bit.ly/20plFmP\r\nhttp://bit.ly/1nGaKDH http://bit.ly/1VKOHXu http://bit.ly/1TCONlg http://bit.ly/1PRp8zu\r\n\r\n\r\ncara / jerawat\r\n\r\nhttp://goo.gl/A3gh1o http://goo.gl/ahVpDo http://goo.gl/x16jPC http://goo.gl/y1yZBZ\r\nhttp://goo.gl/UAwZBd http://goo.gl/4VaPFO http://goo.gl/4bs86Z http://goo.gl/RcNpaG\r\nhttp://goo.gl/oeqTyn http://goo.gl/e4KQr2 http://goo.gl/rk3aA8 http://goo.gl/Eft9Ps\r\nhttp://goo.gl/hPkho9 http://goo.gl/qAAzhK http://goo.gl/i3Wg3g http://goo.gl/lsCrpe\r\nhttp://goo.gl/wPbqOu http://goo.gl/caAYbh http://goo.gl/RrQDxb http://goo.gl/r6MfxA\r\nhttps://goo.gl/UGUSXF http://goo.gl/KaDfg2 http://goo.gl/5ebr2n http://goo.gl/AQGAwy\r\nhttp://goo.gl/QTUi70 http://goo.gl/8of41B http://goo.gl/LRXmzt http://goo.gl/sjvJFV\r\nhttp://goo.gl/IDHh47 http://goo.gl/PXpYIG http://goo.gl/ntz4kA http://goo.gl/suwZKu\r\nhttp://goo.gl/5PfZMS http://goo.gl/sRVOOV http://goo.gl/SIvW94 http://goo.gl/rk99ip\r\nhttp://goo.gl/G7fNJP http://goo.gl/qRdeRl http://goo.gl/ULzbWg http://goo.gl/Tdgqys\r\nhttp://goo.gl/UQfHcy http://goo.gl/jCmE3Y http://goo.gl/ldsl2E http://goo.gl/uB3KGb\r\nhttp://goo.gl/RSbQ6x http://goo.gl/FaC5K8 http://goo.gl/DbXg3X http://goo.gl/KKwLyJ\r\nhttp://goo.gl/nhn0zo http://goo.gl/LrFpsO http://goo.gl/aqu15J http://goo.gl/mMo0S5\r\nhttp://goo.gl/uNvgos http://goo.gl/CJVliF http://goo.gl/hpfU0c http://goo.gl/F7sr9z\r\nhttp://goo.gl/8BCgKG http://goo.gl/vfeQDe http://goo.gl/mbrzBY http://goo.gl/JQQVGp\r\nhttp://goo.gl/drOytt http://goo.gl/nVpd0U http://goo.gl/ZWWbJi http://goo.gl/PDBUiR\r\nhttp://goo.gl/vlsLVj http://goo.gl/PUfMuf http://goo.gl/iTYDzu http://goo.gl/do2QzU\r\nhttp://goo.gl/2BjsR0 http://goo.gl/QsWQ3d http://goo.gl/JQ7uZS http://goo.gl/B84rFE\r\nhttp://goo.gl/kmrnv6 http://goo.gl/4kbsOv http://goo.gl/PbrX2Z http://goo.gl/X1yH1l\r\nhttp://goo.gl/3JYfjc http://goo.gl/8EwmMb http://goo.gl/n67aXX http://goo.gl/CH5M6G\r\nhttp://goo.gl/iq83ED http://goo.gl/yQUjGQ http://goo.gl/V0k37r http://goo.gl/SlhyAb\r\nhttp://goo.gl/EwVWdJ http://goo.gl/xg1lpY http://goo.gl/W92L6S http://goo.gl/M9GcoU\r\nhttp://goo.gl/O5PW7Z http://goo.gl/ouweOE http://goo.gl/Y0mTBE http://goo.gl/Y4mGza\r\nhttp://goo.gl/rrcjH3 http://goo.gl/NMKQ1v http://goo.gl/f7r98I http://goo.gl/sxerfJ\r\nhttp://goo.gl/kv4173 http://goo.gl/g7UmaO http://goo.gl/i1bhYM http://goo.gl/t1NFDV \r\nhttp://goo.gl/f4WdL0 http://goo.gl/EWjtEc

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