Broglie wavelength - calculate electric potential difference

[pbonnie]

Homework Statement

In a TV tube, an electric potential difference accelerates electrons from a rest position towards a screen. Just before striking the screen, the electrons have a wavelength of $1.0 x 10^{-11} m$. Find the electric potential difference.

Homework Equations

$λ = h/mv$
$ΔE_k = qΔV$

The Attempt at a Solution

$v = h/λm = (6.63x10^{-34}Js)/(1.0x10^{-11}m)(9.11x10^{-31})$
$= 7.3 x 10^7 m/s$
I rearranged the second equation to solve for ΔV
$ΔV = ((1/2)(9.11x10^{-31}kg)(7.3x10^7m/s))/(1.60 x 10^-19c)$
$= 2.1 x 10^{-4} V$

I was just wondering if someone could let me know if I'm doing this right? Sorry for not using latex properly, I'm not really sure how to make fractions.

 

[TSny]

Hello.

Your method looks good. But you need to check your calculation of the kinetic energy of the electron.

 

[sonnyfab]

Units

Another good way to see that your calculation went awry is to check your units instead of just writing Volts as the units for the answer.

kg*(m/s)/C are the units on your product in the final line of your calculation before the answer. But Volts are J/C

We know that a Joule is not a kg*m/s, but should be a kg*m²/s².

Hope this helps.

Dr Peter Vaughan
BASIS Peoria Physics

 

[pbonnie]

Ah thank you both very much. I wrote down the 1/2mv^2 in my actual work but forgot to do the calculation.

Thank you:)

 

[TSny]

Good work!

Note that you got a speed of the electron that is about 24% the speed of light. This is encroaching on the domain of relativity. But your non-relativistic answer is accurate to within 2% error.

 

[arnold ruhimbaza]

i think for the Ek formula should be 1/2mv^2 and seems you missed the to square the 7.3E7m/s