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.