Question

Electrons each with momentum 2.24539MeV/c are accelerated through an electric field of strength 4N/C over a distance of 34nm. What is the wavelength of the electron after they pass through the electric field (electron’s speed increases)? Use non-relativistic quantities. (Answer in pm with three sig figs)

Answer 1

So Momentum increased by accelaration due to electric field is

p= V2me Ed

Here e is charge of electron

E is electric field

d = 34 nm

m is mass of electron

So plug in values we get

p = 1.97 x 10-2kg.m/s

In MeV /c

p' = 3.705 x 10-MeV/c

Which is very low compare to initial momentum

So wavelengths of electron is

$\lambda =\frac{h}{p}$

So,

$\lambda =\frac{6.62\times 10^{-34}\times 3\times 10^8}{2.24\times 1.6\times 10^{-13}}$

So,

$\lambda = 8.86\times 10^{-13} m = 0.886pm$