Name: Bohr Atom Model: Frequency of Emitted Radiation
Uploaded: 2019-07-19
Duration: 3 min 54 s
Description: Electrons jump in different energy levels. Let's understand how we can calculate the frequency of emitted and absorbed radiation as electrons transition into...

Question

Write the Bohr's postulates for the hydrogen atom. Derive the formula for the orbital frequency of electron moving in the

n^{th}

orbit of hydrogen atom, using Bohr's postulates.

Accepted Answer

According to Bohr's model, the centripetal force required for the revolution of electrons around the nucleus is provided by the electrostatic force of attraction between the electron and the nucleus.

If $m$ is the mass of electron moving with a velocity $v$ in a circular orbit of radius $r,$ then the necessary centripetal force is $F = \frac{{mv}^{2}}{r} . . . . . . . . . . . . . . . (i)$

Also, the electrostatic force of attraction between the nucleus of charge $(+ Ze)$ and electron of charge $(- e)$ is

$F = \frac{1}{4 {πϵ}_{\circ}} \frac{{Ze}^{2}}{r^{2}} = \frac{{KZe}^{2}}{r^{2}} . . . . . . . . . . . . . . . (ii)$

Where, $K = \frac{1}{4 {πϵ}_{\circ}}$

From $(i)$ and $(ii)$

$\frac{{mv}^{2}}{r} = \frac{{KZe}^{2}}{r^{2}}$

$r = \frac{{KZe}^{2}}{{mv}^{2}} . . . . . . . . . . . (iii)$

Also, one of the Bohr’s postulates states that the electron revolves in stationary orbits where the angular momentum of electron is an integral multiple of $\frac{h}{2 π}$

$mvr = \frac{nh}{2 π}$

Here, $h$ is Planck's constant and $n$ is any positive integer, $1, 2, 3 . . . . . . . .$

$⇒ r = \frac{nh}{2 πvm} . . . . . . . . . . . . . . (iv)$

or $v = \frac{2 {πKZe}^{2}}{nh} . . . . . . . . . . . . . . . . . . . (v)$

Now, we know frequency $(v)$ of electron in Bohr's stationary orbit is given by

$v = rω = r (2 πν)$

$ν = \frac{v}{2 πr}$

From $(v),$ we get

$ν = \frac{v}{2 πr} = \frac{2 πKZe 2}{nh . 2 πr} = \frac{{KZe}^{2}}{nhr}$

$v = \frac{{KZe}^{2}}{nhr}$

Above expression is the orbital frequency of electron moving in the $n^{th}$ orbit of hydrogen atom.

Now, we know the orbital period $(T)$ of the electron moving in the nth orbit of hydrogen atom is related to $(v)$ as $T = \frac{1}{ν}$

$\Rightarrow T = \frac{nhr}{{Ke}^{2}}$

Write the Bohr's postulates for the hydrogen atom. Derive the formula for the orbital frequency of electron moving in the $n^{th}$ orbit of hydrogen atom, using Bohr's postulates.

Important Questions on Atoms

Learn and Prepare for any exam you want !

Write the Bohr's postulates for the hydrogen atom. Derive the formula for the orbital frequency of electron moving in the nth orbit of hydrogen atom, using Bohr's postulates.

Important Questions on Atoms

Learn and Prepare for any exam you want !

Write the Bohr's postulates for the hydrogen atom. Derive the formula for the orbital frequency of electron moving in the $n^{th}$ orbit of hydrogen atom, using Bohr's postulates.