Question

Let r,v and E are the radius of the orbit, speed of the electron and the total energy of the electron respectively. Which of the following quantities are proportional to the quantum number’n’?​

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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Answer 2

Answer:

Hey Mate! Here Is Your 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

Hope this helps you

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