Q11 of 47 Page 1

Obtain the expression for the ratio of the de-Broglie wavelengths associated with the electron orbiting in the second and third excited states of hydrogen atom.

As de Broglie suggested that the wavelength of a matter is associated with its momentum as


Where P is the momentum of matter (mv)


And h is Planck’s constant i.e.


The velocity of an electron following Bohr model is given by



Where Z is the atomic number of hydrogen-like species


And n is the orbit in which the electron is revolving


Speed of electron in 2nd excited state will be


As Z = 1


And n =3



So, momentum in a 2nd excited state will be


P= mv




Therefore then,



Now for 3rd excited state


Speed of electron in a 3rd excited state will be


As Z = 1


And n =4



So, momentum in a 3rd excited state will be


P= mv




So,




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