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

State the postulates of Bohr's theory of hydrogen atom.

Accepted Answer

Bohr's model gives a satisfactory explanation of stable atomic structure and emission of line spectra by a hydrogen atom. He presented his theory in the form of three postulates:

Postulates $1$ : The electron in a hydrogen atom revolves in a circular orbit around the nucleus with the nucleus at the centre of orbit. The necessary centripetal force for circular motion is provided by the electrostatic force of attraction between the positively charged nucleus and negatively charged electron.

Let an electron of mass $m$ revolves with speed $v$ in an orbit of radius $r$ . The charge on the nucleus must be $+ e$ to make the atom electrically neutral. Therefore, Centripetal force = Electrostatic force of attraction.

$\frac{{mv}^{2}}{r} = \frac{1}{4 {πε}_{o}} \frac{e^{2}}{r^{2}}$

Postulate 2 : The electron can revolve without radiating energy only in certain orbits in which the angular momentum of the orbiting electron is equal to an integral multiple of $\frac{h}{2 π}$ , where h is Planck's constant. These orbits are called stable or stationary (or permitted or quantized or Bohr orbits). Thus, angular momentum $L = mvr$ is quantized :

$∴ mvr = n \frac{h}{2 π}$

where $n = 1, 2, 3, . . .$ etc. The integer $n$ is called the principal quantum number, and it denotes the number of the orbit.

Postulate 3: When an electron jumps from orbit of higher energy to an orbit of lower energy, it radiates energy in the form of quanta or photons. The energy of the emitted photon is equal to the difference between energies of two orbits in which transition is taking place.

The radiation of energy is in the form of a photon of energy $hν$ , where $ν$ is the frequency of radiation. If $E_{n}$ and $E_{p}$ are the energies of the electron in the higher energy state and lower energy state.

$∴ hν = E_{n} - E_{p}$

State the postulates of Bohr's theory of hydrogen atom.

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