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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

Verified by Experts

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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