What is the wavelength of llight emitted when the electron in a hydrogen atom undergoes transition from an energy level with n=4 to an energy level with n=2 ?

Explanation

According to Rydberg equation, wave number,
`overline(v)=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
or, `overline(v)=109677[(1)/((2)^(2))-(1)/((4)^(2))]cm^(-1)`
`[R=109677cm^(-1) and n_(2)=4,n_(1)=2]`
or, `overline(v)=109677xx(3)/(16)=20564.43cm^(-1)`
`therefore lamda=(1)/(v)=(1)/(20564.43)cm=4.86xx10^(-5)cm=486xx10^(-7)cm`
`=486xx10^(-9)m=486` nm.