Question

Show that de- Broglie hypothesis of matter wave supports the Bohr’s concept of
stationary orbit.
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Answer 1

The de- Broglie hypothesis of matter wave supports the Bohr’s concept of stationary orbit.

• According to de- Broglie hypothesis, a wave is associated with moving particle which controls the particle in all aspects.
• The wavelength of wave associated with an electron moving with velocity v is given by,
• λ = h/mv ......(1)
• where λ = de- Broglie wavelength, h = Plank's constant m = mass of the particle.
• According to the hypothesis, a stationary orbit is an orbit whose circumference is an integral multiple of wavelength of the wave associated with an electron.
• 2πr = nλ
• λ = 2πr/n ....(2)
• equating (1) and (2), we get,
• h/mv = 2πr/n
• mvr = n (h/2π)
• ∴ Total angular momentum = n (h/2π)
• This is stated by Bohr's postulate about the stable orbits.
• Electrons revolve only in stationary orbits for which the total angular momentum of the revolving electron in an integral multiple of h/2π.