A small particle of massm moves in such a way that the potential energy U = ar^(2) where a is a constant and r is the distance of the particle from the origin. Assuming Bohr's model of quantization of angular momentum and circular orbits, find the radius of n^(th) allowed orbit.

A small particle of massm moves in such a way that the potential energ

1.	A small particle of massm moves in such a way that the potential energy U = ar^(2) where a is a constant and r is the distance of the particle from the origin. Assuming Bohr's model of quantization of angular momentum and circular orbits, find the radius of n^(th) allowed orbit.
Answer» <html><body><p>`n^2`<br/>`n`<br/>`sqrtn`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>/(sqrtn)`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`-1/2 xx P.E.= <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a>.E` <br/>`=-1/2 (- 1/2 mkr^2) = 1/2 mv^2 , mvr = (<a href="https://interviewquestions.tuteehub.com/tag/nh-570695" style="font-weight:bold;" target="_blank" title="Click to know more about NH">NH</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/2pi-1838601" style="font-weight:bold;" target="_blank" title="Click to know more about 2PI">2PI</a>),` <br/>`v^2 = (n^2 h^2)/(4pi^2 m^2 r^2) ,r^4 = (n^2 h^2)/(2pi^2 m^2 k) ` or `r^00 sqrtn`</body></html>