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Grade upto college level Modern Physics

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

13 Years agoGrade upto college level

4 Answers

Arun Kumar

12 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

8 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

8 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

5 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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