1.

One electron is made to revolve around a pro ton and it possesses the least possible energy and another electron is made to revolve around an `alpha`-particle with the same energy. Calculate the ratio of the distances of the electrons from the respective species

Answer» Revolution of an electron around a proton at the closest distance implies that it is a hydrogen atom in its ground state. Similarly, the other particle is `He^+`. The energy of the electron revolving around the nucleus of `He^+` should be -K.
`therefore-k=(-kz^2)/(n^2)`
`therefore n^2=4[thereforeZ=2]`
`thereforen=2`
The ratio of radii of the first orbit of hydrogen to the second orbit of `He^+=(kxx1^2)/((kxx2^2)/2)=1:2`


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