Question

Explain why a hydrogen atom with its electron in the ground state cannot absorb a photon of just any energy when making a transition to the second excited state (n = 3).

Answer 1

Solution :-

Lets calculate the energy needed to excite the electron from ground state level n = 1 to excited state energy level 3

E= -RH [ (1/nf^2)-(1/ni^2)]

E= -2.18*10^-18 J *[(1/3^2)-(1/1^2)]

E= 1.938*10^-18 J

now using the energy lets calculate the wavelength

E= hc/lambda

lambda= hc/E

           = 6.626*10^-34 J.s * 3*10^8 m per s / 1.938*10^-18 J

          = 1.03*10^-7 m

1.03*10^-7 m * 1*10^9 nm / 1 m = 107 nm

so the the wavelength of the photon needed is 107 nm for the excitation of the electron from the n =1 to n = 3

therefore any energy cannot be absoerbed. the specfic wavelength lingh that is 103 nm light will be absorbed.