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A proton, a deuteron and an q-particle h...

A proton, a deuteron and an q-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If `r_(p),r_(d)andr_(alpha)` ro denote respectively the radii of the trajectories of these particles then

A

`r_(alpha) = r_(d) gt r_(p)`

B

`r_(alpha) = r_(d) = r_(p)`

C

`r_(alpha) lt r_(d) lt r_(p)`

D

`r_(alpha) = r_(p) gt r_(d)`

Text Solution

Verified by Experts

The correct Answer is:
D
Radius of the curcular path of a charged particles a magnetic field id given by
`:.(r_(A))/(r_(B))=(sin90^(@))/(sin30^(@))=2orr_(A)=r_(B)orr_(B) < r_(A)" " ( because "kinetic energy",K=(1)/(2)mv^(2))`
For the same value of K and B `:.rprop(sqrtm)/(q)`
`:.r_(p):r_r_(alpha)=(sqrtm_(p))/(qp):(sqrtm_(d))/(qd):(sqrtm_(alpha))/(qalpha)`
`=(sqrtm)/(e):(sqrt2m)/(e):(sqrt4m)/(2e)=1:sqrt2:1`
`impliesr_(alpha)=r_(p) < r_(d)`
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Knowledge Check

  • A proton, a deuteron and an alpha -particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If r_p , r_d and r_alpha denote respectively the radii of the trajectories of these particles then :-

    A
    `r_alpha = r_d gt r_p`
    B
    `r_alpha =r_d = r_p`
    C
    `r_alpha lt r_d lt r_p`
    D
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    `r_(alpha)=r_pltr_d`
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