Same in optics, for resolve small target’s detail, we need a smaller ‘wavelength’.

According to de-Broglie, a matter has wavelength:

\lambda = h / p

Therefore, a smaller wavelength requires larger momentum and momentum is related with energy by:

p = \sqrt {2 m c^2 T + T^2}

Thus, that’s why particle physics need larger and larger machines to produce higher and higher energy.

To reach 1 fm , electron should has kinetic energy around 100MeV, or momentum around 100MeV/c.

From Heisenberg’s uncertainty principle,

x p \geq \hbar


pc \geq \hbar c / x = 200MeV fm / x

Therefore, to reach x ~ 1 fm, momentum should at least 200 MeV/c.

The above estimations are consistence.