Question

In Bohr Model Of Hydrogen Atom, Let R, V And E Represent The Radius Of Orbit, Speed Of The Electron And Total Energy Of Electron In Particular Quantum State ‘N’ Respectively. Which Of Following Quantities Are Directly Proportional To Quantum Number N? a) vR b)RE c)v/E d)R/E

Answer 1

ANSWER

The velocity of revolving electron is: v=2nhϵ0e2

The Rydberg's constant is: R=8ϵ02h3cme4

Hence, vR=2nhϵ0e2×8ϵ02h3cme4

vR=16nh4ϵ03cme6

Since, n,h, ϵ0, m,c and e are constant. 

Hence, the vR is inversely proportional to principal quantum number(n). 

The energy of an electron is:

E=8n2h2ϵ02−me4

Hence, Ev=8n2h2ϵ02−me4

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