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# Using Bohr'S Postulates, Derive the Expression for the Total Energy of the Electron in the Stationary States of the Hydrogen Atom ? - Physics

ConceptBohr'S Model for Hydrogen Atom

#### Question

Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?

#### Solution

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. =

$\frac{m v^2}{2} - \frac{e^2}{4 \pi\epsilon_0 r}$
Substituting the values, we get:
E_n =-e^2/( 8πe_0) (m/n^2)((2π)/h)^2
⇒ E_n = (me^4)/(8π^2∈_0^2 h^2)
∴ E_n = - (2.18 xx 10^-18)/n^2j
E_n = 13.6/n_2 eV
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Solution Using Bohr'S Postulates, Derive the Expression for the Total Energy of the Electron in the Stationary States of the Hydrogen Atom ? Concept: Bohr'S Model for Hydrogen Atom.
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