A positronium consists of an electron and a positron revolving about their common centre of mass. Calculate the separation between the electron and positron in their first excited state:

Answer

(i) ` r_(0)=(2h^(2))/(pi^(2)m)xx(4piepsilon_(0))/(e^(2))=4.23Å`
(ii) `(1)/(2)((e^(2)pi)/(4pi epsilon_(0)h))J=3.4 eV`

Explanation

From Bohr hypothesis
`(mv^(2))/(r//2)=(1)/(4piepsilon_(0)).(e^(2))/(r ^(2))`
`rArr 2mv^(2)r=(1)/(4piepsilon_(0)).e^(2)`.....(1)
and `(nh)/(2pi)=mvr`.....(2)
from (1) and (2)
`v=(1)/(4piepsilon_(0)).(e^(2))/(nh)xx(2pi)/(2)`
`(1)/(4piepsilon_(0))/(e^(2)pi).(nh)`

(i) `r=(nh)/(2pi).(1)/(m).(4piepsilon_(0).n^(2)h^(2))/(pime^(2))`
(ii) `KE=(1)/(2)mv^(2)=(1)/(2)m((e^(2))/(4epsilon_(0)h))=3.4 eV`