If the wavelength of the `n^(th)` line of Lyman series is equal to the de-broglie wavelength of electron in initial orbit of a hydrogen like element `(Z=11)`. Find the value of `n`.

Answer

`n=24`

Explanation

If the wavelength of the `n^(th)` line of Lyman series is equal to the de-broglie wavelength of electron in initial orbit
`(1)/(lambda)=RZ^(2)(1-(1)/((n+1)^(2)))=(1)/((h//mv))=(mv)/(h)=(mvr)/(hr)=`
`((n+1)h)/(2pihr)=(n+1)/(2pir)` putting, `r=(r_(0)(n+1)^(2))/(Z)`
`(1)/(lambda)=RZ^(2)(1-(1)/((n+1)^(2)))=((n+1)Z)/(2pir_(0)(n+1)^(2))" " rArr(n+1)-(1)/((n+1))=(1)/(2pir_(0)ZR)=(1)/(2pixx11xx0.53xx10^(-10)xx1.1xx10^(7))`
`=(1000)/(2pixx12.1xx0.53)=24.8" "rArr(n+1)=25" "rArrn=24`