An electron in the first excited state of H atom absorbed a photon and further excited. The de broglie wavelength of the electron in this state is found to be `13.4` Å. Find the wavelength of the photon absorbed by the electron in angstroms. Also find the longest and the shortest wavelength emitted when this electron de-excited back to the ground state.

Answer

4

Explanation

Let the electron jumps from first excited state (n = 2) to n = n.
De-Broglie wavelength of `e^(-)` in nth orbit `= 13.4Å`
`rArr" "(h)/(mv)=13.4Å" "rArr" "(6.6xx10^(-34))/(9.1xx10^(-31)kgxxV_(n))=13.4xx10^(-10)m" "rArr" "V_(n)=0.54xx10^(6)ms^(-1)`
`rArr" "2.18xx10^(6)(z)/(n)=0.54xx10^(6)" (Z = 1 for H) "rArr" "n=(2.18)/(0.54)=4`