Suppose we wish to use a mass spectrometer to measure the mass m of the 238U+ io
ID: 1414262 • Letter: S
Question
Suppose we wish to use a mass spectrometer to measure the mass m of the 238U+ ion. Assume a source of 238U+ ions exists and that the ions initially move slowly. We want the ions to move at a high speed v in the mass spectrometer. To accelerate the ions to speed v, we use the electric field between the plates of a capacitor. The ions now have speeds roughly equal to v, but because their initial speeds varied somewhat, there is a spread. We want to select ions with speeds very close to v and reject the rest. To do so, we pass the beam of ions through a velocity selector, in which the combination of uniform electric and magnetic fields (E and B, respectively) will allow the passage of only those ions that have a particular speed. The rest of the ions will be deflected into the plates and will therefore not be able to exit. The trajectory of ions that enter the velocity selector with speeds less than the selected v is shown below.
Explanation / Answer
for magnetic field region,
e v B = m v^2 / (D/2)
e B = 2 m v / D
v = e B D / 2 m ..........Ans
for selected velocity,
Eletric force = magnetic force
qE = q v B
E = vB
E= (e B D / 2 m)(B) = e B^2 D / 2m .........Ans