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The Bohr theory of hydrogen atom spectrum

From Equations (2) and (3) by eliminating v,

Thus electrons can orbit in circles of radius :r0, 4r0, 9r0, 16r0, ......... where r = , the electron m p e2 is prohibited from occupying the intervening space between these orbits.

The energy E of an electron in any 'stationary' orbit must be,

Equations (5) and (6) represent the quantized orbits and the energy of electrons in 'stationary' orbits. Now, let an electron jump from a higher orbit n2 to a lower orbit n1 (n2 and n1 are natural numbers; n2 > n1), then the energy lost by the electron is given by,

   DE    =   En2    -    En1


But, according to Equation (4),

          DE    =    hn

For a visible spectrum: n1 = 2, n2 = 3, 4, 5, 6,.....

Comparing (9A) with (1), we must have

When R.H.S is calculated it precisely turns out to be 1.097 ´ 107 m-1 (!)


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32 : Bohr's theory of hydrogen atom and its spectrum

Chapter 33

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