When beryllium-7 ions (m = 11.65 × 10-27 kg) pass through a mass spectrometer, a uniform magnetic field of 0.205 T curves their path directly to the center of the detector, as in the drawing. For the same accelerating potential difference, what magnetic field should be used to send beryllium-10 ions (m = 16.63 × 10-27 kg) to the same location in the detector? Both types of ions are singly ionized (q = +e).

ratio =0.3075 T

Explanation:

The magnetic field B creates a force on a moving charge such that

Now this causes a centripetal acceleration

 so

...........(i)

 ...............(ii)

If  accelerating potential V is  same and  then  kinetic energy equals the potential energy difference

     put these value in equation (ii)

simplifying we get  

for same location r will be same in both case

     ..............(iii)

   ..........(iv)

 dividing (iv) and (iii) equation we get

so on solving we get  

             =0.3075 T

when it gains or loses electrons

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