3.a. By using the de Broglie relation, derive the Bohr condition mvr = nh. 3.b.Use this expression to show that the allowed electron energy states in Hydrogen atom can be written mk² e 2h? n? E, 3.c.Find the wavelength of photon that is emitted when the electron in a Hydrogen atom undergoes a transition from n=3 to n=1.

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3.a. By using the de Broglie relation, derive the Bohr condition mvr = nh.
3.b.Use this expression to show that the allowed electron energy states in Hydrogen atom can be
written
mk? e
En
2k² r?
3.c.Find the wavelength of photon that is emitted when the electron in a Hydrogen atom undergoes
a transition from n=3 to n=1.
Transcribed Image Text:3.a. By using the de Broglie relation, derive the Bohr condition mvr = nh. 3.b.Use this expression to show that the allowed electron energy states in Hydrogen atom can be written mk? e En 2k² r? 3.c.Find the wavelength of photon that is emitted when the electron in a Hydrogen atom undergoes a transition from n=3 to n=1.
Expert Solution
Step 1

a. Allowed orbits are those in which an electron constructively interfere with itself.

2πr=nλ condition for constructive interferencen is integerPutting debroglie wavelengthλ=hp=hmv2πr=nhmvmvr=nh2πmvr=nh, where n=1,2,3...b.    Fc= centripetal forceFe= electrostatic forceFc= Femv2r=ke2r2mv2=ke2rusing r=nhmvmv2=ke2mvnhv=nhnhmke2r=n2h2mke2E=T+U, T=12mv2=12ke2rU=-ke2rE=12ke2r-ke2rE=-12ke2rSubstituting the value of r, we get=-12ke2n2h2mke2=-12k2e4mn2h2

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