Question

It may seem strange that the selected velocity does not depend on either the mass or the charge of the particle. (For example, would the velocity of a neutral particle be selected by passage through this device?) The explanation of this is that the mass and the charge control the resolution of the device--particles with the wrong velocity will be accelerated away from the straight line and will not pass through the exit slit. If the acceleration depends strongly on the velocity, then particles with just slightly wrong velocities will feel a substantial transverse acceleration and will not exit the selector. Because the acceleration depends on the mass and charge, these influence the sharpness (resolution) of the transmitted particles.

Assume that you want a velocity selector that will allow particles of velocity v⃗ to pass straight through without deflection while also providing the best possible velocity resolution. You set the electric and magnetic fields to select the velocity v. To obtain the best possible velocity resolution (the narrowest distribution of velocities of the transmitted particles) you would want to use particles with __________.

a) both q and m large
b) q large and m small
c) q small and m large
d) both q and m small

Answer 1

The values of q must be large and m small to obtain the best possible velocity resolution (the narrowest distribution of velocities of the transmitted particles).

Step-by-step explanation:

Based on Newton's law of motion, the formula for force is as below:

f = ma ---------------------------1

But a = a = v²/r

so, f = mv²/r -------------------2

Also, f = qE --------------------3

From the equations above, it is observed that the values of q must be large and m small to obtain the best possible velocity resolution (the narrowest distribution of velocities of the transmitted particles).