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An electron moves around the nucleus in ...

An electron moves around the nucleus in a hydrogen of radius `0*51 Å` with a velocity of `2xx10^6m//s`. Calculate (i) the equivalent current due to orbital motion, (ii) magnetic field produced at the centre of nucleus. (iii) magnetic moment associated with electron.

Text Solution

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Here, `r=0*51 Å=0*51xx10^(-10)m`
`v=2xx10^6m//s`
(i) `I=e/T=(e)/(2pir//v)=(ev)/(2pir)`
`=(1*6xx10^(-19)xx2xx10^6)/(2xx3*14xx0*51xx10^(-10))=10^-4A`
(ii) `B=(mu_0I)/(2r)=(4pixx10^-7xx10^-4)/(2xx0*51xx10^(-10))=1*23T`
(iii) `M=IA=(ev)/(2pir)xxpir^2=1/2evr`
`=1/2xx1*6xx10^(-19)xx2xx10^6xx0*51xx10^(-10)`
`=8*16xx10^(-25)Am^2`
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