Heisenberg's Uncertainty Principle
- Particles behaving as waves and waves behaving as particles results in a need to look at events in a new way
- So far, calculations show that even electrons can be delt with in precise ways.
- Heisenberg in 1927 suggested that there is always some uncertainty in determining exact positions and speeds (energies) for electrons
- The uncertainty was due to the quantum mechanical nature of subatomic particles.
- Suppose we try to determine the position of an electron in an atom.
- To determine position, we must irradiate the electron with light in order to see the electron.
- Momentum of a Photon is
P = h/ l
- With light, we can locate things only to the accuracy equal to about the wavelength of light.
- Since electrons are very small, we must therefore use a very small wavelength of light to locate the electron.
- If the wavelength is small, then frequency is large (C = f l), and momentum (P = h/ l) is large.
- The energy of the photon (E = hf) is therefore also large.
- high energy, high momentum photons, when they contact an electron, will transfer significant momentum and energy to the electron
- As a result, we can locate were the electron was, but not know its new momentum or energy.
- The smaller the wavelength is, the larger the momentum and energy is for the photon. Therefore, we know accurately the location, but not momentum, since the momentum will be severely affected.
- If we use a larger wavelength so that momentum is smaller (P = h/l) and energy is smaller
- (E = (hc)/l), then the momentum of the electron is less affected (we know it more accurately), but we don't know the position as well.
- As a result of this, Heisenberg stated his Heisenberg uncertainty principle
- Heisenberg uncertainty principle - We are unable to know the position and momentum of an electron with unlimited accuracy.
DX DP ³ h/(2p)
DE DT ³ h/(2p)
DP = mDv
- In these equations Dv = uncertainty in velocity, DP = uncertainty in momentum, DE = uncertainty in energy, DT = uncertainty in time interval, and DX = uncertainty in position.
- The equation DE DT³ h/(2p) tells us that the smaller the time interval, the greater the uncertainty in energy.
- Uncertainty is unimportant for large size objects.
- Consider a 1 kg object with momentum P = mv.