Determining e/m of electron lab

[Aziza]

In our lab we determined the charge to mass ratio e/m of electron by creating electron beam and making it spin in a circle using a magnetic field from helmholtz coils. According to the pasco lab manual for this experiment, the velocity of the electrons in the beam will be lower than theoretical (because of nonuniform acceleration and collisions with helium atoms which made the circle glow), and thus the lab manual says that our measured e/m will be HIGHER than theoretical...

But I thought our measured should be LOWER than theoretical? Since (e/m)=(v^2)/(2ΔV) where v is velocity and ΔV is accelerating voltage, then lower v for the same ΔV should yield lower e/m...

 

[Jasso]

Think about it. The lab makes the simplifying assumption that the velocity is uniform throughout the trip of the circular path; as noted, the electron slows down because of interaction with the rarefied gas in the chamber. This means that the true average velocity is lower than the assumed average velocity. However, it is the assumed (initial) velocity that you plug into the equation you gave to determine your measured e/m; the theoretical e/m is the one where you plug in the true average velocity and will be lower than what you measure.

 

[Aziza]

Think about it. The lab makes the simplifying assumption that the velocity is uniform throughout the trip of the circular path; as noted, the electron slows down because of interaction with the rarefied gas in the chamber. This means that the true average velocity is lower than the assumed average velocity. However, it is the assumed (initial) velocity that you plug into the equation you gave to determine your measured e/m; the theoretical e/m is the one where you plug in the true average velocity and will be lower than what you measure.

ok I am still confused...
you say
"However, it is the assumed (initial) velocity that you plug into the equation you gave to determine your measured e/m; the theoretical e/m is the one where you plug in the true average velocity and will be lower than what you measure."

but the assumed/measured velocity is lower. thus measured e/m is lower. thus theoretical is higher than measured, not lower...

 

[mfb]

Maybe "the velocity of the electrons in the beam will be lower than theoretical" means that you overestimate the velocity - the real velocity is lower than the calculated one (based on magnetic field and radius), so the real e/m is lower, too. This corresponds to "your measured e/m is too high".

 

[Aziza]

Maybe "the velocity of the electrons in the beam will be lower than theoretical" means that you overestimate the velocity - the real velocity is lower than the calculated one (based on magnetic field and radius), so the real e/m is lower, too. This corresponds to "your measured e/m is too high".

but if real velocity is lower, then my MEASURED e/m will be lower, not the real e/m. the real e/m is independent of my measured (lower) velocity..

 

[Jasso]

You aren't measuring the velocity, you are measuring the radius of curvature of the beam.

When you find the curvature, you plug that in, along with other values into an equation to find the e/m. For a given velocity and magnetic field strength, the e/m is given by $e/m = v / (r B)$. So as the velocity of the electrons decrease, the radius of the beam increases making a spiraling shape instead of a perfect circle. However, the lab doesn't take into account that the velocity decreases, it assumes that the velocity is higher than it really is and this higher velocity is the one used to calculate the e/m. That means that the e/m you calculate will be higher than it would normally be without the energy loss.