Suppose the electric field between the electric plates in the mass spectrometer

Question

Suppose the electric field between the electric plates in the mass spectrometer shown above is E = 2.36 x 104 V/m and the magnetic fields B = B' = 0.578 T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate the atomic masses, multiply the mass numbers by 1.66 x 10-27 kg.) How far apart are the lines formed by the singly-charged ions of each type on the photographic film?
Separation d =

How far apart are the lines if the ions are doubly-charged?

Separation d =

Please include solution as well as answer.

Explanation / Answer

velocity v = E / B = 2.36 *10^4 V/m / 0.578 T v = 4.083044982698962 *10^4 m/s Under circular motion mv^2 / r = qvB radius of the circular orbit r = mv / qB Here m = mass , v = vvelocity q = charge= 1.6*10^-19 C, B = magnetic field = 0.709 T diameter of the circular orbit for 82 Kr D1 = 2r1 = m1 *v / qB diameter of the circular orbit for 84 Kr D2 = 2r2 = m2 *v / qB diameter of the circular orbit for 86 Kr D3 = 2r3 = m3 *v / qB distance between the 82 Kr and 84 Kr d = m2 *v / qB - m1 *v / qB = v / qB (m2 -m1) .........(1)

here m2 = 13*1.67*10^-27 kg , m1 = 12*1.67*10^-27 kg plug all values (1) we get d = mm similarly distance between the
d = m3 *v / qB - m2 *v / qB = v / qB (m3 -m2) here m3 = 14*1.67*10^-27 kg plug all values we get d = ..........mm diameter of the circular orbit for 84 Kr D2 = 2r2 = m2 *v / qB diameter of the circular orbit for 86 Kr D3 = 2r3 = m3 *v / qB diameter of the circular orbit for 86 Kr D3 = 2r3 = m3 *v / qB distance between the 82 Kr and 84 Kr d = m2 *v / qB - m1 *v / qB = v / qB (m2 -m1) .........(1)

here m2 = 13*1.67*10^-27 kg , m1 = 12*1.67*10^-27 kg plug all values (1) we get d = mm similarly distance between the
d = m3 *v / qB - m2 *v / qB = v / qB (m3 -m2) here m3 = 14*1.67*10^-27 kg plug all values we get d = ..........mm

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