De Broglie equation explain the assumption made by Bohr?

Question

Give a description with a clearly labelled diagram to describe how the de Broglie hypothesis explains the assumptions made by Bohr for the hydrogen atom.
I understand the concepts but just can't piece them together in this way :/

Answer 1

I'm not entirely sure that I understand what you want here but I'll give you what I can. I can't give you a diagram [ unless you send me a personal email, then I can send you one as an attachment].

Lets start with Bohr's atomic postulates, which he used to explain the stability of the electron orbits.

1) An atom can exist in any one of several, special orbits, with no emmision of radiation. These orbits are called stationary states, and are characterised by values of orbital, angular momentum given by



L = m v r = n (h/2π)

m = mass; v = tangential velocity; r = radius of orbit; n = principle quantum number; h = Plank's constant.



2) Using the Plank/Einstein relation



E = h f

h = Planks constant; f = frequency



when an electron absorbs or emits a photon of this energy, it can jump between orbits.



De Broglie went on to show that all matter particles have wave-like propeties.

He performed a series of remarkably simple looking substitutions as follows:

Starting with Einstein's famous equation he had



E = mc^2 = mc * c



mc = mass * velocity = momentum,p.



E = p c

c = f λ



E = p (f λ)

So

h f = p (f λ)



λ = h / p



For electrons in an atom, De Broglie then proposed that the wave-like nature manifests itself in the form of standing waves. In each orbit, or shell, when the electron moves round the nucleus, its associated wave is stationary, hence the standing wave.

In this situation, only certain, discrete frequencies will have a wavelength that will exactly fit around the nucleus at each distance from it.. The standing waves are given by



2πr = nλ



But, from the De Broglie equation we have

λ = h / p = h / mv



So

n (h / mv) = 2πr



n (h / 2π) = m v r

which is Bohr's quantum postulate.



That's about all I can give you. The diagram would just be a circle or radius r, superimposed on which would be a wavy line, drawn around the circumference, with a whole number of waves.

I hope this helps.

Answer 2

ucd engineering?

Answer 3

Here's the basic rundown. I'll leave the diagrams to you:



* Bohr proposed that electrons, for whatever reason, could only orbit atoms at certain fixed radii. This explained why they only ever had certain energy levels, and only certain transitions took place. It also let him predict the exact energy levels for hydrogen. However, he couldn't actually explain why they only orbited at this fixed distance.



* De Broglie proposed that particles could also behave as waves, and that applied to electrons. In this model, an electron only remains in a stable orbit if the orbital path was an integer number of wavelengths (i.e. it could be one or two wavelengths, but not 1.5, for example). This would explain why only certain energy levels were allowed and others were not.

Answer 4

Bohr postulated that electrons move only in stationary orbits.Classical EM theory a charge in accelerated motion cannot be in stationary orbit.

Debacle postulated that stationary orbits are those orbits in which electron's wavelength is such that it forms a standing wave in the orbit.ie

Let the radius of orbit be r and wavelength of De broglie wave be lambda then

2.pi.r=n.lambda

This idea helped Bohr to give the atomic model of Hydrogen Atom.