Share
Notifications

View all notifications

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

Login
Create free account


      Forgot password?
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^2`j
`E_n = 13.6/n_2 eV`
  Is there an error in this question or solution?

APPEARS IN

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.
S
View in app×