In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1). If `n gt gt 1,` the frequency of radiation emitted is proportional to

Options

A. `(1)/(n)`
B. `(1)/(n^(2))`
C. `(1)/(n^(3)2)`
D. `(1)/(n^(3)2)`

Answer

B, D

Explanation

`DeltaE=hv`
`v=(DeltaE)/(h)=k[(1)/((n-1)^(2))-(1)/(n^(2))]=(k2n)/(n^(2)(n-1)^(2))`
`~~(2K)/(n^(3))prop(1)/(n^(3))`
`r=(mv)/(eB)rArr(r^(2)e^(2)B^(2))/(2)=(m^(2)v^(2))/(2)`
`(r^(2)e^(2)B^(2))/(2m)=(mv^(2))/(2)`
`1.89-phi=(r^(2)e^(2)B^(2)1)/(2m)(1)/(e)eV=(r^(2)eB^(2))/(2m)eV=(100xx10^(-6)xx1.6xx10^(-19)xx9xx10^(-8))/(2xx9.1xx10^(-31))`
`phi=1.89-(1.6xx9)/(2xx9.1)`
`=1.89=0.79~=1.1 eV`