Tau 09 - Uncertainty Principle!
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Transcript of Tau 09 - Uncertainty Principle!
THE UNCERTAINTY PRINCIPLE
Guerrero. Rombaoa. Kabigting.IV-Tau Group 9
It is impossible to know both the exact position and exact momentum of an object at the same
time.
Werner Heisenberg, 1927Nobel Prize Awardee in Physics (1932)
IN QUANTUM PHYSICS…
A particle is described by a wave.
Position - where the wave is concentrated
Momentum - the wavelength
The position is uncertain to the degree that the wave is spread out.
The momentum is uncertain to the degree that the wavelength is ill-defined.
POSITION (Δx)
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.
MOMENTUM (Δp)
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.
Momentum is uncertain
Position is uncertain
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
”
Using the formula…
ΔxΔp ≥ h⁄4π
If Δx 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 Δx will be large.
Where Δx is the change in position, Δp is the change in momentum and
h is Planck’s constant
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.
ΔxΔp ≥ ħ⁄2
The Uncertainty Principle also holds true for the particle approach!
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
ΔEΔt ≥ ħ⁄2
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.