An electron in the hydrogen atom absorbs energy and jumps to the 4th orbit. It jumps back to the ground state in steps e.g., from 4th to 3rd orbit, then from 3rd to 2nd orbit and finally to the ground state etc.
If the ionization of the hydrogen atom in the ground state is `13.6 eV`. The longest wavelength of the radiation required to remove the electron from Bohr's first orbit will be approximately

Options

A. `612 Å`
B. `712 Å`
C. `812 Å`
D. `912 Å`

Answer

D

Explanation

Ionization energy `= 13.6 xx 1.602 xx 10^(-19) J`
`=21.78 xx 10^(-19) J`
`E = hv = (hc)/(lamda)`
`:. lamda = (hc)/(E) = ((6.626 xx 10^(-34) Js) (3 xx 10^(8) ms^(-1)))/(21.78 xx 10^(-19) J)`
`= 9.12 xx 10^(-8) m = 912 Å`