Question

Problem-2 (10 points): The electron in the hydrogen atom makes a transition from the first excited state (n 2) to the ground state (n = 1). Calculate the wavelength of the radiation emitted in this transition, will you consider this particular wavelength to be very well suited for the determination of the crystal structure of a metal single crystal? Justify your answer

Answer 1

For a Hydrogen atom,

E₂ = - (13.6/2²)eV = - 3.4 eV

and E₁ = - 13.6 eV

so, E₂ - E₁ = 10.2 eV

equate this to the energy of a photon since a photon of this much energy must be released from the transition.

so, $\lambda = \frac{hc}{(E_2-E_1)} = \frac{6.626\times 10^{-34}(3\times 10^8)}{10.2\times 1.6\times 10^{-19}} = 121.80 nm$ . This lies in the UV range and it is thus not useful for determination of crystal structure as the dimensions of crytals planes are much smaller than this wavelength.