If the electron gains the energy for the jump from energy level `E_(1)` to energy level `E_(3)` by absorbing light, what light wavelength is required ?

Explanation

KEY IDEAS
(1) If light is to transfer energy to the electron, the transfer must be by photon absorption. (2) The photon.s energy must equal the energy difference `DeltaE` between the initial energy level of the electron and a higher level, according to Eq. 38 - 6 `(hf=DeltaE)`. Otherwise, a photon can not be absorbed.
Wavelength : Substituting `c//lambda` for f, we can rewrite Eq. 36-6 as
`lambda=(hc)/(DeltaE)`.
For the energy difference `DeltaE_(31)` we found in (b), this equation gives us
`lambda=(hc)/(DeltaE_(31))`
`=((6.63xx10^(-34)J.s)(2.998xx10^(8)m//s))/(4.83xx10^(-17)J)`
`=4.12xx10^(-9)m.`