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 0.75 T uniform magnetic field at a speed of 2.7 105 m/s. If a fragment has a mass 70 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?

Atoms are ionized2. Ions of diferent and accelerated. Ions masses follow paths of a particular velocity of different radii are selected to enter n.. the spectrometer. 2r Detector 3. Only ions of a particular mass reach the exit slit and continue to the detector.

Explanation / Answer

q = charge = 1.602 x 10^-19 Coulombs

The magnetic force exerted on the ion when it enters the mass spectrometer is

F(magnetic) = q * v * B

Where

q = charge = 1.602 x 10^-19 C
v = protein ion's velocity = 2.7 x 10^5 m/s
B = strength of the magnetic field = 0.75 T

the direction of the magnetic field and velocity are perpendicular.

here the magnetic force is balanced by the centripetal force of the particle traveling in a circle :

F(centripetal) = m*v^2 / r

m = mass of ion = 70 * mass of proton = 116.9*10^-27 kg

When we equate the two forces we get:

m*v^2 / r = q*v*B

or

r = (m*v) / (q*B)

But the distance from the entrance of the ion to the point where it exits the magnetic field is 2*r (the DIAMETER of the circle is makes). Therefore:

D = distance = 2*r = (2*m*v) / (q*B)

D = 0.526 m = 52.6 cm

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