A mass spectrometer similar to the one in the figure below is designed to separa

Question

A mass spectrometer similar to the one in the figure below is designed to separate protein fragments. The fragments are ionized by removing a single electron and then enter a 0.87 T uniform magnetic field at a speed of 3.9 x 105 m/s. If a fragment has a mass of 65 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?

A mass spectrometer similar to the one in the figure below is designed to separate protein fragments. The fragments are ionized by removing a single electron and then enter a 0.87 T uniform magnetic field at a speed of 3.9 x 10^5 m/s. If a fragment has a mass of 65 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?

Explanation / Answer

KE = PE

0.5 mv^2 = eV

or v = sqrt(2eV/m)

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

where m = mass o the charged particle

v = velocity,   r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , r = mv/qB

so r = 65*1.67e-27 * 3.9e5 /(1.6e-19 * 0.87)

r = 0.304 m

so total disatnce = diameter = 2r = 2*0.304 =0.608 m   = 60.8 cm

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