The second experiment is similar to the mass spectrometer. An electron beam is f
ID: 2147968 • Letter: T
Question
The second experiment is similar to the mass spectrometer. An electron beam is first accelerated by a voltage source, and then passes into a region of uniform magnetic field. The experiment is performed in a vacuum tube which is filled with a small amount of phosphor gas so the arc of the electron bean can be seen and measured. Find a new expression for the charge to mass ratio, which this time will also include the radius of the arc the electron beam would make.Hint: Your final expressions should not contain the velocity of the beam, as it cannot be directly measured. Think about work and energy to find a way to remove velocity from the equations. Provide some voltages, currents, magnetic fields, etc. for each of your equations to give no deflection, and hence the proper charge to mass ratio (at least two examples).
Explanation / Answer
Radius is given by :
r = m x v / q x B -(1)
Since, velocity can't be measured we use Energy conservation
e V = 0.5 x m x v2
v = (2 x e x V) / m - (2)
Repplacing (2) in (1)
r = (1/B) x [(2 x m x V) / q]
where V is the potential difference