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Example · Example 1

Q.State the two postulates of Bohr's model of the hydrogen atom that

(a) quantise the angular momentum of the electron and
(b) fix the energy of a stationary orbit.
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Bohr's model rests on a small number of postulates, of which two directly quantise the electron's motion.

Quantisation of angular momentum. Only those circular orbits are allowed for which the electron's orbital angular momentum is an integral multiple of h/2πh/2\pi:

mvr=n h2π,n=1,2,3,…mvr = n\,\frac{h}{2\pi}, \qquad n = 1, 2, 3, \ldots

Here mm is the electron's mass, vv its speed, rr the orbit radius, hh Planck's constant, and nn the principal quantum number labelling the orbit. Only these particular combinations of rr and vv are permitted; every other orbit is forbidden.

Stationary (non-radiating) orbits. As long as the electron remains in one of these allowed orbits, it does not emit electromagnetic radiation, even though classical theory says an accelerating charge (and a circling electron is accelerating, since its direction keeps changing) must continuously radiate energy and spiral inward. Bohr simply postulated that this classical expectation does not apply to these particular orbits, which is exactly what keeps the atom stable and allows the electron to occupy a fixed orbit indefinitely.

Energy is emitted or absorbed only when the electron jumps between two allowed orbits, with the photon's energy exactly equal to the energy difference between them -- this third postulate is what reproduces the hydrogen line spectrum.

✓Final answer

The two postulates are: (i) the electron can move only in orbits for which its angular momentum equals an integral multiple of h/2πh/2\pi, i.e. mvr=n(h/2π)mvr = n(h/2\pi); and (ii) as long as the electron stays in such a stationary orbit, it does not lose energy by radiation.

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