2. It is impossible to know both the exact position and exact momentum of an object at the same time . Werner Heisenberg, 1927 Nobel Prize Awardee in Physics (1932)
3.
4. POSITION ( Δ x ) When is it certain? NARROW wave group GREATER range of λ WELL-DEFINED position This means that position is uncertain for conditions opposite to those mentioned above.
5. MOMENTUM ( Δ p ) When is it certain? WIDE wave group WELL-DEFINED λ MORE PRECISE momentum This means that momentum is uncertain for conditions opposite to those mentioned above.
7. What did you notice? OPPOSITE TRENDS!! for position & momentum Certain physical quantities can’t both have precise values at the same time. The narrower the probability distribution for one, the wider it is for the other. “ X ”
8. Using the formula… Δ x Δ p ≥ h ⁄4π If Δ x is small (corresponding to a narrow wave group), then Δp will be large. If Δp is reduced, then a broad wave group is inevitable and Δ x will be large. Where Δ x is the change in position, Δp is the change in momentum and h is Planck’s constant
9. Sample Problem ħ = h/2π A measurement establishes the position of a proton with an accuracy of 1.00 x 10 -11 m. Find the uncertainty in the proton’s position 1.00s later. Assume v<<c. ħ (H-bar) is the basic unit of angular momentum. Δ x Δ p ≥ ħ ⁄2
11. Energy and Time Energy may be in the form of EM waves, so the limited time available restricts the accuracy with which frequency of the waves can be determined. another pair of quantities that follow the uncertainty principle Δ E Δ t ≥ ħ ⁄2
12. More applications A typical nucleus is about 5.0 x 10 -15 m in radius. Use the uncertainty principle to place a lower limit on the energy an electron must have if it is to be part of the nucleus. on the atomic level only * * An “excited” atom gives up excess energy by emitting a photon of a certain frequency. The average period that elapses between excitation and time it radiates is 1.0 x 10 -8 s. Find the inherent uncertainty in the frequency.
