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The electric potential between a proton and an electron is given by V =V_0 In r/r_(0)" where "r_(0) is a constant. Asuming Bohr'a model to be applicable, write variation of, r_(n) with n, n being the principal quantum number: -- |
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Answer» `r_(N) alpha n` But `F=-(d V)/(dr)=(e V_(0))/(r)` But `F=-(d V)/(dr)=(eV_(0))/(R)` `RARR (mv^(2))/(r)=(e V_(0))/(r) (therefore F=(mv^2)/(r))` `therefore v=sqrt((e V_(0))/(m))` But `mv r_(n) =(NH)/(2pi)` `rArr m^(2)v^(2)r_(n)^(2)=(n^(2)H^(2))/(4pi^(2))` `m^(2) (e V_(0))/(m) .r_(n)^(2)=(n^(2)h^(2))/(4pi)` `r_(n)^(2)=(n^(2)h^(2))/(4pi meV_(0)) rArr r_(n)^(2) alpha n^(2)` `r_(n) alpha n` |
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