(a) Write Bohr's postulates of hydrogen atomic model.
(b) Explain the origin of spectral lines using Bohr's atomic model.
(c) Write De Broglie's explanation of Bohr's second postulate of quantization.
Answers
Explanation:
First Postulate: Electron revolves round the nucleus in discrete circular orbits called stationary orbits without emission of radiant energy. These orbits are called stable orbits or non-radiating orbits.
Second Postulate: Electrons revolve around the nucleus only in orbits in which their angular momentum is an integral multiple of h/2π.
Third Postulate: When an electron makes a transition from one of its non-radiating orbits to another of lower energy, a photon is emitted having energy equal to the energy difference between the two states. The frequency of the emitted photon is then given by, v=
h
E
i
−E
f
(b)Bohr tells us that the electrons in the Hydrogen atom can only occupy discrete orbits around the nucleus (not at any distance from it but at certain specific, quantized, positions or radial distances each one corresponding to an energetic state of your H atom) where they do not radiate energy.
When the electron moves from one allowed orbit to another it emits or absorbs photons of energy matching exactly the separation between the energies of the given orbits (emission/absorption spectrum).
We see these photons as lines of coloured light (the Balmer Series, for example) in emission or dark lines in absorption
(c)What is de-broglie explanation of Bohr's second postulate?
Bohr’s 2nd postulate tells us that electrons orbit the nucleus only in those orbits for which the angular momentum is an integral multiple of nh/2(pi). However the question arises is why? why should an electron only orbit a nucleus depending on the angular momentum of the orbit. The answer to that question was answerd by de broglie. By that time de broglie established his wave mater duality principle. From it we come to know of matter waves and how there wavelengths are inversly proportional to the mass of the body and the velocity of the body, by the relation:
(wavelength) = h /mv
thus we come to know about why massive macro objects dont show wave nature. the wave length is too small and negligable.
what de broglie did was he included his wave nature principle in bohrs 2nd prostulate. He imagined the circumference of the orbit as a string and extending it in a straight line applied his concept and derived the same equation of angular momentum as bohr. I provided the maths and the explaination below.
2(pi)r = n(wavelength)
2(pi)r = nh/mv
*here 2(pi)r is the circumference of the orbit = the length of the string and h/mv is the wavelength equation from debroglie (which I provided abover) and n is the number of wavelengths. What he wanted to see was how many wavelengths can fit inside a orbit of circumference 2(pi)r.
mvr = nh/2(pi)
L = nh/2(pi)
Solving the equation we get to Bohr’s 2nd postulate equation.
The explaination concluded by de broglie was, that wavelengths of mater waves was quantised. This means The electrons can exists in those orbits which had a complete set of n number of wavelengths (matter wave wavelengths depend on the mass and velocity of the electron) where n is a whole number (and not an integer like 1.5 or 2.7 etc). And since each of those orbits will have a constant angular momentum, hence the phenomenon can also be explained as, the electrons will orbit the nucleus in those orbits for which the angular momentum is nh/2(pi). where n is again a whole number.
Hope I helped.. :)
How can you explain Bohr's second postulate?
Using the de Broglie hypothesis, how does one explain Bohr's second postulate of quantization of orbital angular momentum?
Is the proof regarding Bohr's second postulate true?
How does de Broglie hypothesis explain the stationary orbits?
What is the experimental verification of de Broglie's hypothesis?
Bohr assumed quantization of angular momentum of electron revolving round in a specified orbit. de Broglie explained “why the angular momentum is quantized” using the wave-particle duality. De-Broglie assumed that the wavelength associated with the electron, is an integral number of wavelengths must fit in the circumference of an orbit and derived the expression for angular momentum.
Starting from the idea that the circumference of the circular orbit must be an integral number of wavelengths:
2πr = nλ
Taking the wavelength to be the de Broglie wavelength (λ = h/p), this becomes:
2πr = nh/p
The momentum, p, is simply mv as long as we're talking about non-relativistic speeds, so this becomes:
2πr = nh/mv
Rearranging this a little gives the Bohr relationship:
Ln= mvr = nh/2π
Answer:
1.Bohr's model of the hydrogen atom is based on three postulates: (1) an electron moves around the nucleus in a circular orbit, (2) an electron's angular momentum in the orbit is quantized, and (3) the change in an electron's energy as it makes a quantum jump from one orbit to another is always accompanied by the ...
Explanation: