Need help In the arrangement shown (rendition of a mass spectrometer), an ionize

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In the arrangement shown (rendition of a mass spectrometer), an ionized gas particle of mass m = 3.33 Times 1017 kg and charge magnitude q = 3.204 Times 10-19 C is produced essentially at rest. The ion is then accelerated by potential difference V = 100 v and allowed to enter a magnetic field B. In the field it moves in a semicircle, striking a photographic plate at a distance 2r from the entry position, where r = 0.88 cm. a) Calculate the magnetic field strength. b) Is the ion positive or negatively charged? c) The photographic plate is 22 cm in length. The maximum charge an ion can have is 5.6 Times 10-18 C. What is the largest possible mass that can be measured by this machine?

Explanation / Answer

a)

0.5 m v^2 = q V

==> v = sqrt(2*3.204e-19*100/3.33e-27) = 138720 m/s

q v B = m v^2/r

==> B = m v/(q r) = 3.33e-27*138720/(3.204e-19*0.88e-2) = 0.164 T

b)

negative

c)

r = 11 cm

==> q v B = m v^2/r ==> v = r q B/m = 0.11*5.6e-18*0.16384/m = 1.0092544e-19/m

==> 0.5 m v^2 = q V ==> 0.5 * m * ( 1.0092544e-19/m)^2 = 5.6e-18 * 100

==> m = 9.09 * 10^-24 Kg

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