A narrow beam of singly charged carbon ions, moving at a constant velocity of `6.0 X10^4 ms^(-1),` is sent perpendicularly in a rectangular region having uniform magnetic field B=0.5 T . It is found that two beams emerge from the field in the backward derection, the separations from the incident beam being 3.0 cm and 3.5cm. Identify the isotopes persent in the ion beam. Take the mass of an ion = `A(1.6 X10^(-27)` kg, where A is the mass number.

Explanation

` u = 6 xx 10^(4) m/s , B = 0.5 T` ,
` rArr r_(1)= (3)/(2) = 1.5 cm , r_(2) = (35)/(2) cm `
`rArr r_(1) = (mu)/(qB)`
rArr ` 1.5 xx 10^(-2) = (m_(1_ xx 6 xx 10^(4) )/(6 xx 1.6 xx 10 ^(-10) xx 0.5) `
` rArr m_(1) = 1.2 xx 10 ^(-36)`
` = 12 xx 10^(-36)`
Hence carbon ratine = 2 (for carbon )
The laolopes used are ^(12)C _(0) and ^(14)C`