Why does uncertainty in position measurement equal the photon wavelength?

[Gunman]

Homework Statement

"If the photon has a short wavelength, and therefore a large momentum, the position can be measured accurately. But the photon will be scattered in a random direction, transferring a large and uncertain amount of momentum to the electron"

Homework Equations

I am unsure about this formula: [Uncertainty in the measurement ~ Wavelength of photon]

The Attempt at a Solution

How is this so? Is it because the electron can be anywhere along the wave before it scatters the wave? Therefore inducing the uncertainty?

Thanks in advance.

 

[NYSportsguy]

Remember Momentum (p) = mass * velocity. Shorts wavelengths mean that photons needs more kinetic energy to get from point A to B because they go up and down so much (in shorter, choppier wavelengths).

What you are trying to find out is called the photoelectric effect, which Einstein came up with in 1905. Basically any photon of light that has a certain frequency (shorter wavelength = higher frequency) will have more kinetic energy and thus higher momentum.

Any photon above the "thresh hold frequency" will have enough quantized energy in it to be absorbed by an electron in an atom of say, some metal. Thus when it absorbs this photon with a high frequency it will fly off the atom and into the air with whatever kinetic energy it has left.

The "uncertainty" part comes in due to a physicist named Heisenberg (with the help of Niels Bohr). They said that any electron that flys off can can land anywhere. It is impossible to predict both the exact position and the momentum of any given electron or atom simultaneously. If we accurately measure one, the other accuracy of measurement will suffer and vice-versa.

In quantum mechanics, we can only predict using "probability" where an electron will land or where the atoms of molecules will be positioned next because of the randomness and haphazard style with which molecules move. Heisenberg and various double-slit model tests prove this to be fact. Einstein was uneasy with this fact and principle and refused to believe that God would "roll the dice" in cause and effect in quantum physics.

However, Bohr and Heisenberg to this day are considered correct while Einstein is not in this case.

 

[Gunman]

Thanks for explaining what the uncertainty principle was for.=)
Just curious, how do you actually find the probability of the various positions it may land at? And the momemtum? If the photon is absorbed by the electron then how do you go about measuring the momentum and position of electron? And if the photon does return because it does not correspond to the energy difference between the levels, then the electron position and momentum are not affected by the photon? And the I don't get the part about how having shorter wavelength helps to decrease the uncertainty of the new position of electron.
Thanks for taking the time to answer.