A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the nth orbit and the particle's speed v in the orbit depend on n as
- r n2/3; v n1/3
- r n4/3; v n-1/3
- r n1/3; v n1/3
- r n1/3; v n2/3
Answer
(1) r n2/3; v n1/3
Solution
Centripetal force is provided by F: mv2r = F v2 = Frm ... (i)
Bohr's quantisation: mvr = nh2 v = nh2 mr ... (ii)
From (i) and (ii): n2h24 2m2r2 = Frm r3 = n2h24 2mF
r n2/3
From (i): v r1/2 n1/3
Answer: (1)