Question

How did Louis de Broglie explain Bohr's postulate for quantized angular momentum?

• A. He hypothesized that even electron is a wave in its corresponding orbit whose stable existence is only possible if the electron wave is a standing wave.
• B. He proposed that an electron exists as a wave in its circular orbits and these waves need not be stationary
• C. He proposed that for an electron to exist as a wave, the circumference of the orbit must be an integral multiple of
• D. He proposed that for an electron to exist as a wave, the circumference of the orbit must be an integral multiple of

Answer 1

Answer: (A), (C)

The correct options are
A He hypothesized that even electron is a wave in its corresponding orbit whose stable existence is only possible if the electron wave is a standing wave.
C He proposed that for an electron to exist as a wave, the circumference of the orbit must be an integral multiple of

According to Bohr, the electrons do not radiate any energy when they are in stable orbits.

Louis de Broglie suggested that just like light, even matter exhibit wave like behavior which was proved to true by Davisson and Germer with the help of electron diffraction experiment. We did that in last chapter.So de Broglie hypothesized that if the electrons have to exist as waves, they must be standing/stationary so as their energy is confined between the two nodes. (Remember why standing wave/stationary wave got such a name).
If they exist as a travelling wave they will interfere destructively and the energy will be lost pretty soon.

Also, for such a stationary wave to exist the circumference must be an integral multiple of the wavelength.

As you can see above that only when $2\pi r=n\lambda$ then constructive interference happens and the wave perfectly fits the circle
If the condition is not true then the wave will destructively interfere with itself and the entire wave will die off. Which will mean that the electron will no longer exists, which doesn’t happen