Based on Maxwell's theory of electrodynamics, an electron travelling in a circle ought to emit radiation with a frequency equal to its frequency of revolution. If this rule is applied, what would be the wavelength of the radiation emitted by a hydrogen atom in its ground state?

Step-by-step solution

The frequency of revolution of an electron in its orbit is given by f = v 2 r . According to Maxwell's theory of electrodynamics, the frequency of the emitted radiation is equal to the frequency of revolution of the electron. The wavelength of the emitted radiation is = c f = 2 r c v . For a hydrogen atom in its ground state ( n=1 ): Radius of the first orbit, r = 0.529 10⁻¹⁰ m Velocity of the electron, v = 2.18 10^6 m/s Speed of light, c = 3 10^8 m/s Substituting these values into the expression for wavelength: =