What is the de Broglie wavelength of an electron accelerated by 75V?

AI Thread Summary
The discussion revolves around calculating the de Broglie wavelength of an electron accelerated by a potential difference of 75V. The participant correctly identifies the relevant equations, including the relationship between momentum and wavelength, and the kinetic energy derived from the voltage. They convert the voltage to energy but initially arrive at an incorrect wavelength of 1.4E21 m. Other contributors suggest that the equations are correct, and the error likely lies in numerical calculations, indicating the correct wavelength should be 1.4E-10 m. The focus is on verifying calculations rather than the theoretical framework.
Brendanphys
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Homework Statement



This is a problem I did during a test, and I am looking it over to see what I did wrong..

1. An Electron is accelerated by a potential difference of 75V. What is the de Broglie wavelength

Homework Equations



P = h/λ
Ek = 1/2mv^2
eV = 1.6E-19

The Attempt at a Solution



P = h/λ
λ = h/p (1)

Ek = 1/2mv^2
(2Ek/m)^1/2 (2)

Sub (1) into (2)
λ = h/p
λ = h/m((2Ek/m)^1/2)

I figured 75V = 75*eV = 75*(1.6E-19) = 1.2E-17J
So 1.2E-17J = Ek

I Plugged in all the known values into
λ = h/m((2Ek/m)^1/2)
and got the answer as: 1.4E21

Any clues as to what I did wrong? I assume it has something to do with my volt conversion, any help would be greatly appreciated.
 
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I think its just a math error. The energy is fine.

Mass of a electron is 9.10938188*10^-31.

Try putting it into your calculator again.
 
There's nothing wrong with your equations. You probably just calculated the numbers incorrectly. Try again, and you should get 1.4e-10 m.
 

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