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According to Bohrs theory of hydrogen atom angular momentum of electron in any orbit is directly proportional to square root of the radius of orbit. HOW?

Yogita Bang , 12 Years ago
Grade upto college level
anser 4 Answers
Arun Kumar

Last Activity: 10 Years ago

Hello Student

Angular momentum = mvr
v=root(ZKe^2/mr)
So Angular Momentum = mvr=root(ZKe^2*r*m)
and that how its proportional to square root of the radius

Thanks & Regards
Arun Kumar
Askiitians Faculty
IIT Delhi

Ashish Sahani

Last Activity: 7 Years ago

We know that r=n^2/Z. ............(1)For Hydrogen, Z=1SoEquation (1) became r=n^2orn=√r. ..................(2)We also know thatAngular momentum =nh/2π. ......(3)From eq. (2)We can writeAngular momentum is directly proportional to √r

Ashish Sahani

Last Activity: 7 Years ago

We know that r=n^2/Z. ............(1)For Hydrogen, Z=1SoEquation (1) became r=n^2orn=√r. ..................(2)We also know thatAngular momentum =nh/2π. ......(3)From eq. (2) [n =√r]We can writeAngular momentum is directly proportional to √r

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the answer to your question.
 
We know that angular momentum = r x linear momentum = r x P
= r x 2m(KE)
= r x 2m(KZe2/2r)
= KZe2mr
Hence angular momentum, L ∝ r
 
Thanks and regards,
Kushagra

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