I have this question:

An electron with Energy $E = 40 eV$ hits a potential barrier with $E_0 = 30 eV$. What is the wavelength of the electron after hitting the potential barrier?

I worked from the energy $E = p\cdot v \Rightarrow m_e \cdot E = p^2$ and combined it with the DeBroglie Wavelength $\lambda \cdot p = h$ which yields

$$ \lambda = \frac{h}{\sqrt{m_e \cdot (E-E_0)}} $$

However, the sample solution says the wave number is

$$ k = \frac{2\pi}{\lambda} = \frac{\sqrt{2\cdot m_e \cdot (E-E_0)}}{\hbar} $$

Which is exactly what I got, except for the $2$ inside the root.

Where does that factor come from? Why is my lacking of it wrong?

Note: I tagged this homework although it's not really homework, but homework-like head-scratching.

  • 2
    $\begingroup$ Not to worry, the homework tag is entirely appropriate here. $\endgroup$
    – David Z
    Aug 26 '12 at 17:36

Hint to the question(v1): The electron travels at non-relativistic speed. What is the non-relativistic formula for kinetic energy of a point particle?

  • $\begingroup$ D'oh, silly me. I always neglect those pesky constants. $\endgroup$
    – bitmask
    Aug 26 '12 at 18:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.