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 of (Figure 1) is 2.98×104V/mand the magnetic fields B=B=0.71T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by 1.67 ×1027kg.)

Part A

How far apart are the lines formed by the singly charged ions of mass numbers 12 and 13 on the photographic film?

Part B

How far apart are the lines formed by the singly charged ions of mass numbers 13 and 14 on the photographic film?

Explanation / Answer

as charge passes through spectrometer,

Fnet = Fb - Fe = 0

q v B = q E => v = E / B = (2.98 x 10^4) / (0.71)

v = 4.20x 10^4 m/s

after that charge will move in circular path in the magnetic field region,

for that ,

q v B = m v^2 / r

r = m v / q B

m , q and B is same for all the charge .

and m = n M = n (1.67 x 10^-17 kg)

so r = (1.67 x 10^-27 x n) (4.20 x 10^4) / (1.6 x 10^-19) (0.71)

r = 6.08 x 10^-4 n

(A) delta(r) = (13 - 12) (6.08 x 10^-4)

= 6.08 x 10^-4 m

(B) Ans: 6.08 x 10^-4 m

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