If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å and (ii) R = 10  Å .

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    Vishal Baghel | Contributor-Level 10

    3 months ago

    This is a Long Answer Type Questions as classified in NCERT Exemplar

    Explanation- in this type of situation centripetal force is balanced by electrostatic force

    So mv2/r= -ke2/r2

    According to bohr postuates

    Mvr = h when n=1

    On solving n  h 2 m 2 r 2 1 r = k e 2 / r 2

    So after solving r= 0.51A0

    So potential energy  k e 2 r = -27.2eV , KE= mv2/2

    = 1 2 m h 2 r 2 = h 2 m r 2 = + 13.6 e V

    But if R

    If R>>r the electron moves inside the sphere with radius r’

    Charge inside r’4=e r ' 3 R 3

    So r’ = h 2 m k e 2 R 3 r ' 3

    So r’4= 0.51A0R3

    = 510(A0)4

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Kindly go through the solution

 

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