Calculating Electron Speed in Potential Difference of 25.0 V

[strawberrysk8]

Homework Statement

Electrons from a heated cathode are accelerated through a potential difference of 25.0 V. Calculate the speed of the electrons escaping through a hole in the anode.

Homework Equations

v = (2eV/m)^(1/2)

The Attempt at a Solution

v = (2*25*1.759*10^11)^(1/2) = 2.97*10^6 m/s

but this answer is wrong. why?

 

[Redbelly98]

What are the units for each number you use in the calculation? Perhaps the units are not consistent.

 

[strawberrysk8]

v = (2* 25V * 1.759*10^11 C/kg) ^(1/2) = 2.97*10^6 m/s

(VC/kg)^(1/2) = m/s

or

VC/kg = m^2/s^2

is that true?

 

[Redbelly98]

Okay, I agree with your answer, including the number of significant figures. I wasn't familiar with the value of e/m.

Hmmm ... since the calculated answer is 2.9655... *10^6 m/s, maybe try 2.96*10^6 m/s. They might have done some intermediate rounding off that changed their final answer slightly.

 

[strawberrysk8]

that still turned out to be wrong. maybe i am using the wrong formula. this problem deals with a cathode and anode from a helm's coil. any suggestions?

 

[Redbelly98]

I'm unfamiliar with a helm's coil (or do you mean Helmholtz coil?).

Your formula is correct for electrons with zero, or at least negligible, initial kinetic energy at the cathode.
(Substitute eV = ½ m v² in the equation to verify it, if you wish.)

Does anything in the problem statement, or in the textbook, indicate a nonzero initial speed for the electrons? If not, I am stumped ... does somebody else have any ideas?

 

[strawberrysk8]

thank you so much! i had been typing the answer wrong. the computer did not want the answer in scientific notation. so your advice was correct. thank you

 

[Redbelly98]

Your welcome!

Computers often use a different form of scientific notation. Instead of typing 2.97*10^6, it would be 2.76e6

You might try that out on the next problem, just to see if the computer recognizes it.