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Singly charged magnesium (A=24) ions are...

Singly charged magnesium (A=24) ions are accelerated to kinetic energy `2 ke V` and are projected perpendicularly into a magnetic field B of magnitude 0.6 T. (a) Find the radius of the circle formed by the ions. (b) If there are also singly charged ions of the isotope magnesium-26, what would be the radius for these particles?

Text Solution

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The radius is given by
`r = (mv)/(qB)=sqrt(2mK)/(qB)` for `^24Mg ions, m=24Xm =24Xm_q` approximately and
`q=1.6 xx 10^(-19)C.` Putting the values, `r= sqrt(2X24X1.67X10^(-27)kgX2000X1.6 X10^(-19) J)/(1.6xx10^(-19)Cxx0.6 T)`
=0.53 m = 5.3cm
. For `^26mg,` the radius r will be given by
`r = sqrt(2m'K)/(qB)`
or `r =rsqrt(m)/(m) = 5.3cm sqrt(26)/(24) = 5.5cm.`
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