A Bohr hydrogen atom undergoes a transition `n=5rarrn=4` and emits a photon of frequency v. Frequency of circular motion of electron in n = 4 orbit is `V_(4)`. Find the ratio `v//v_(4).(54)/(25N)`, where N is an integer find N

Answer

`0003`

Explanation

`0003`
`E_(n)=-(mz^(2)e^(4))/(8 epsilon_(0)^(2)n^(2)h^(2))`
so , `hv=+(mz^(2)e^(4))/(8 epsilon_(0)^(2)h^(2))[(1)/(16)-(1)/(25)]`
`:. v=(mz^(2)e^(4))/(8 epsilon_(0)^(2)h^(3))[(9)/(16xx25)] " " ...(1)`
and frequency `v_(4)=(1)/(T)=(v)/(2pir)=((ze^(2))/(2 epsilon_(0)nh))(1)/(2pi)((pi m z e^(2))/(epsilon_(0)h^(2)n^(2)))=(z^(2)e^(4)m)/(4 epsilon_(0)^(2)n^(3)h^(3)) " " ....(2)`
`:. v//v_(4)=18//25`