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प्रश्न
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
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उत्तर
According to Bohr’s 2nd postulate, we have : `L_n= mv_nr_n =(nh)/(2π)`
where,
n = principle quantum
vn = speed of the moving electron in the nth orbit
rn = radius of the nthorbit
The electrostatic force of attraction between the electron and the nucleus provides the necessary centripetal force to the electron.
\[\frac{m v^2}{r} = \frac{1}{4 \pi\epsilon_0}\frac{e^2}{r^2}\]
`V_n = e/(sqrt4π∈_0 mr_n)`
`∴ V_n = 1/n e^2/(4π∈_0)1/((h/(2π))`
`r_n =(n^2/m)(h/(2π))^2(4π∈_0)/e^2 `
Total energy, En = K.E. + P.E. =
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