Question

SO an alpha particle of mas 6.68*10^-27 kg has a wavelength of 0.1nm. What is the voltage driving this particle? What is its energy?

I use wavelength= h/p , but the energy of the particle is below 1 volt and it makes no sense, what am i doing wrong?

Answer 1

I'm not sure I understand what you're asking when you say "what is the voltage driving this particle". There can't be an electric field or else the momentum and wavelength of the particle would constantly change. Do you mean what voltage was used to accelerate the particle from rest?

Answer 2

Well, i didnt specify that this alpha particle is inside a alpha particle scanning microscope, and the voltage that drives them out of the source tip if constant.

Answer 3

Well indeed, it seems i still got the right answer

Answer 4

Ah. Yes then, that's what I needed to know. I calculate a momentum of
\[ p = 6.63 \cdot 10^{-34} \space kgm/s\]
if its mass is
\[ m = 6.68 \cdot 10^{-27} \space kg\]
then its velocity is
\[v \approx 992 \space m/s\]
which is nowhere near relativistic, so we don't have to worry about any of that business. If that's the case, the kinetic energy is
\[T = \frac{1}{2} mv^2 = 3.29 \cdot 10^{-21} \space J \approx 20.5 \space meV\]
And since the charge of an alpha particle is 2e, this corresponds to a voltage of
\[\Delta V \approx 10.25 \space mV\]