Question

How did de Broglie hypothesis lead to bohr's quantum condition of atomic orbits?

Answer 1

In quantum mechanics, matter is believed to behave both like a particle and a wave at the sub-microscopic level.
But when we goes inside the subatomic level, things begin to get more complicated, and matter doesn't always exhibit the particle behavior that we expect.
in subatomic level every matter behave like wave and particle.
so according plank ,which is give theory about wave is that the energy of photon (which is intermediate particle of light) is directly proportional to it frequency
and proportionality constant is h(plank constant )
E = h*nu
now according to Albert Einstein which give for particle, energy of particle is equal to
E =mc ^2.
both equation for energy so both are equal
mc ^2 = h*nu
Rutherford discovered nucleus ,but it can not explain all properties of atoms
Rutherford use all theory classically
but it fail to explain hydrogen spectra.
so bohr use de broglie hypothesis to explain the orbit of electrons
so bohr theory is dominant in quantum mechanics
because de broglie is quantized the energy in the form of wave
wave is quantized by photon.