Suppose the electric field between the plates P and P\' in the mass spectrometer

Question

Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.90

Suppose the electric field between the plates P and P' in the mass spectrometer in following figure is 1.9010^4 V/m V/m and the magnetic field in both regions is 0.691T T .(Figure 1) If the source contains the three isotopes of krypton, 82Kr,84Kr , and 86Kr , and the ions are singly charged, find the distance between the two adjaicent lines formed by the three isotopes on the photographic plate. Assume the atomic masses of the isotopes (in atomic mass units) are equal to their mass numbers, 82, 84, and 86. (One atomic mass unit = 1u u = 1.6610?27 kg.) Express your answer using two significant figures.

Explanation / Answer

First we need the velocity by v = E/B

v = (1.9 X 104)/(.691)

v = 27496 m/s

Then apply r = mv/qB for each...

r = (82)(1.66 X 10-27)(27496)/(1.6 X 10-19)(.691)

r = .0339 m and the diameter will be twice that = .0677 m

For the next...

r = (84)(1.66 X 10-27)(27496)/(1.6 X 10-19)(.691)

r = .0347 m and the diameter will be twice that = .06936 m

For the last one...

r = (86)(1.66 X 10-27)(27496)/(1.6 X 10-19)(.691)

r = .0355 m and the diameter will be twice that = .071 m

The distances between are...

.071 - .06936 = 1.66 X 10-3 m which is 1.66 mm

.06936 - .0677 = 1.66 X 10-3 m which is 1.66 mm

So the distance separations are the same.

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