Using Bohr’s second postulate of quantisation of orbital

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atoms

#1

(i) Using Bohr’s second postulate of quantisation of orbital, angular momentum, show that the circumference of the electron in the rath orbital state in H-atom is ra times the de-Broglie wavelength associated with it.
(ii) The electron in H-atom is initially in the . third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?


#2

(i) Bohr’s second postulate states that the electron revolves around the nucleus in certain privileged orbit which satisfy certain quantum condition that angular momentum of an electron is an integral multiple of h / 2$\pi$ , where h is Planck’s constant.
i.e. L = mvr = nh / 2 $\pi$
where, m = mass of electron, v = speed of electron and r = radius of orbit of electron.
2 $\pi$ r = n (h/mv)
Circumference of electron in nth orbit = n x de - broglie wavelength associated with electron.
(ii) Given, the electron in H-atom is initially in third excited state.
n = 4
And the total number of spectral lines of an atom that can exist is given by the relation = n(n-1)/ 2
Here,n=4
So, number of spectral lines = 4 (4-1)/ 2 = 4 x 3/2 = 6
Hence, when a H-atom moves from third excited state to ground state, it emits six spectral lines.