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

A uniform magnetic filed `B` exists in a region. An electron is given velocity perpendicular to the magnetic field. Assuming Bohr's quantization rule for angular momentum.
Calculate the minimum possible speed of the electron.

A

`sqrt((heB)/(nm^(2)))`

B

`sqrt((he)/(2piBm^(2)))`

C

`sqrt((h.eB)/(2piB))`

D

`sqrt((hem^(2))/(2piB))`

Text Solution

Verified by Experts

The correct Answer is:
C
`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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