According to the Heisenberg uncertainty principle, it is impossible to know the exact position *and* momentum of a particle at the same time. The more precisely you know one, the less precisely you know the other. Since a photon has momentum equal to `p=h//lambda`, it can alter the path of an electron when it collides with it. But to measure the position or momentum of an electron, you *have* to shoot photons at it. The very act of looking at the particle in this way changes the results. We are left with two options:

- Use low-energy photons (long wavelength) for precise momentum.
- Use high-energy photons (short wavelength) for precise position.

The product of the absolute uncertainties of position and speed satisfies

`Delta xDelta v >= h/(2pim)`,

where `Delta x` and `Delta v` are the absolute uncertainties of the position, measured in metres (m), and of the speed, measured in metres per second (m/s), respectively, and where *h* is Planck’s constant and *m* represents the mass of the particle, measured in kilograms (kg).

If we know the speed of an electron to within 1.0 m/s, how precisely can we know its position?

Solving the inequality for the uncertainty of position, we have

`Delta x >= h/(2pimDelta v) = (6.63xx10^-34\ "J/s")/(2(3.14)(9.11xx10^-31\ "kg")(1.0\ "m/s")`,

which evaluates to

`Delta x >= 1.2xx10^-4\ "m"`.

We are therefore off by at least 1.2 × 10^{−4} m for the position, which is quite a lot considering that this number is about 100 billion times larger than the radius of the electron—it’s sort of like saying that you know the position of your friend: “he’s somewhere in the solar system.”