हाइड्रोजन सदृश कोई आयन n = 2 से n = 1 तक के संक्रमण में `2.467xx10^(7)`Hz आवृत्ति के विकिरण उत्सर्जित करता है । संक्रमण n = 3 से n = 1 में उत्सर्जित विकिरण की आवृत्ति ज्ञात करो ।

Explanation

`(1)/(lamda) = R[(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
`(n_(1) = 1 n_(2) = 2) v = (c)/(lamda)`
`(v_(1))/(c) = R [(1)/(1^(2)) - (1)/(2^(2))] (v)/(c) = (1)/(lamda)`
`(v_(1))/(c) = (R)[(1)/(1) - (1)/(4)]`
`(v_(1))/(c) = R [(3)/(4)]` ...(i)
`n_(1) = 1 "तथा" n_(2) = 3` के लिए
`(v_(2))/(c) = R [(1)/(1^(2)) - (1)/(3^(2))]`
`v_(2)/(c) = R[1 - (1)/(9)]R`
`(v_(2))/(c) = (8R)/(9)` ...(ii)
समी. (i) में समी. (ii) का भाग करने पर
`(v_(2))/(v_(1)) = ((8)/(9))/((3)/(4))`
`(v_(2))/(v_(1)) = (8xx4)/(3xx9)`
`v_(2) = (8xx4)/(3xx9)v_(1)`
`v_(2) = (32)/(27) xx2.467 xx 10^(7)`Hz
`v_(2) = 1.18 xx 2.467 xx 10^(7)Hz`
`v_(2) = 2.92 xx 10^(7)Hz`