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(i) Calculate the first three energy lev...

(i) Calculate the first three energy levels for positronium.
(ii) Fine the wavelength of the `H_(a)` line `(3 rarr2"transition")` of positronium.

Text Solution

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In positromium electron and positron revolve around their centre of mass
`(1)/(4 pepsilon_(0))(e^(2))/(r^(2))=(mv^(2))/(r//2)`.......(1)
`(nh)/(2pi)=2xxmv_(k//2)`
From (1) & (2)
`V=(1)/(2).(1)/(4 piepsilon_(0)).(e^(2))/(nh)xx2p=(e^(2))/(4 epsilon_(0)nh)`
`TE= -(1)/(2) mv^(2)xx2= -m (e^(4))/(16 epsilon_(0)^(2)n^(2)h^(2))`
`= -6.8(1)/(n^(2))eV`
(i) `E_(1)= -6.8 ev`
`E_(2)= -6.8xx(1)/(2^(2))eV= -1.70 eV`
`E_(3)= -6.8xx(1)/(3^(2))eV= -0.76-(-1.70)eV`
The corresponding wave length
`lambda(1.24xx10^(4))/(0.94)Å=1313Å`
(i) `-6.8eV, -1.7 eV, -0.76 eV`, (ii) `1313Å`
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