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Bohr’s Atomic Model

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge Ze (called hydrogen-like atom)

Bohr’s model is based on the following postulates

  • Bohr postulated that an electron in an atom can move around the nucleus in certain circular stable orbits without emitting radiations.
  • Bohr found that the magnitude of the electron’s Angular momentum is quantized i.e.,
    where n = 1, 2, 3, ..... each value of n corresponds to a permitted value of the orbit radius.
    rn = Radius of nth orbit, vn = corresponding speed
  • The radiation of energy occurs only when an electron jumps from one permitted orbit to another.
    When electron jumps from higher energy orbit (E2) to lower energy orbit (E1), then difference of energies of these orbits, i.e., E2E1 emits in the form of photon. But if electron goes from E1 to E2 it absorbs the same amount of energy.

Drawbacks of Bohr’s atomic model

  • It is valid only for one electron atoms, e.g., H, He+, Li+2, Na+1, etc.
  • Orbits were taken as circular but according to Sommerfield these are elliptical.
  • Intensity of spectral lines could not be explained.
  • Nucleus was taken as stationary but it also rotates on its own axis.
  • It could not be explained the minute structure in spectrum line.
  • This does not explain the Zeeman effect (splitting up of spectral lines in magnetic field) and Stark effect (splitting up in electric field).
  • This does not explain the doublets in the spectrum of some of the atoms like sodium (5890 Å and 5896 Å).

Bohr’s Orbits (for Hydrogen and H2-Like Atoms)

Radius of orbit For an electron around a stationary nucleus the electrostatics force of attraction provides the necessary centripetal force, i.e.,
Fig. 6
From (i) and (ii), radius of nth orbit
⇒ 102252.png
Speed of electron From the above relations, speed of electron in nth orbit can be calculated as,
where c = speed of light 3 × 108 m/s.

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