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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`. |
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Answer» Correct Answer - `n=24` 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` |
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