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A uniform magnetic field B exists in a r...

A uniform magnetic field `B` exists in a region. An electrons projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate
(a) the smallest possible radius of the electrons
(b) the radius of the nth orbit and
(c) the minimum possible speed of the electron.

A

`sqrt((nh)/(2pieB))`

B

`sqrt((nheB)/(2pi))`

C

`sqrt((nhe)/(2piB))`

D

`sqrt((nhB)/(2pie))`

Text Solution

Verified by Experts

The correct Answer is:
A
`evB=(mv^(2))/(r )" "rArrr=(mv)/(eB)`
`mvr=(nh)/(2pi)`....(2)
`rArr r^(2)=(nh)/(2pie)" "(1)/(B)`
`r_(n)=sqrt((nh)/(2pieB))`
`v=(nh)/(2pi).(1)/(mr)=(nh)/(2pi)(1)/(m)sqrt((2pieB)/(nh))=sqrt((nh.eB)/(2pim^(2)))`
`v_(min)sqrt((h.eB)/(2pim^(2)))`
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