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In a hydrogen like atom electron make transition from an energy level with quantun number n to another with quantum numbe (n-1). If ngtgt1, the frequency of radiatioi emitted is proportional to .....

Answer»

`(1)/(n^(3))`
`(1)/(n)`
`(1)/(n^(2))`
`(1)/(n^(3/2))`

Solution :`(1)/(lamda_(ik))=R((1)/(n_(K)^(2))-(1)/(n_(i)^(2)))`
`(f_(ik))/(c)=R((1)/((n-1)^(2))-(1)/(n^(2)))""[:.c=lamda_(ik)f_(ik)]`
`=R[(1)/(n^(2)(1-(1)/(n))^(2))-(1)/(n^(2))]`
`R=[(1)/(n^(2)){(1-(1)/(n))^(-2)-1}]`
`=R[(1)/(n^(2)){1+(2)/(n)-1}]`
First two TERMS of binomial EXPANSION.
`R=[(2)/(n^(3))]`
`f_(ik)=(2Rc)/(n^(3))`
`:.f_(ik)PROP(1)/(n^(3))""` [2 Rc is constant]
`:.FPROP(1)/(n^(3))`


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