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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?

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? 

Grade:upto college level

4 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 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
21 Points
6 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
21 Points
6 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
askIITians Faculty 628 Points
3 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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