Illustrating the Problem Described by Heisenberg's Uncertainty Principle Even a t an elementary level any discussion of the wave-mechanical theory of atomic structure usually involves mention of Heisenberg's Uncertainty Principle. This states that, far a moving particle, the uncertainty Ap in the particle's momentum p and the uncertainty Ay in its position y, where both p and y are measured a t the same time, are linked such that Ap Ay > h/4a, where h is Planck's constant. In simple terms, if we try t o define precisely the position of the particle, we must sacrifice information about its mamentum (or velocity). If we have exact data on its velocity, we cannot a t the same time expect t o know exactly where i t is located in
.
.~
4
5
SDBEB. ~
'l'he concept of being unablr to measure sirnulwnwusly h.th the positiimand vel~rityoia particle as precwly a.wcchoosc is adiflicult one to grasp imcr it is conlrarv to our everyday rxprrirnce in the marn,iwpir w d d . I n his book "The .Myitmuua Universe" (('am. I ~ C (:niversifv P Press. I.ondon. 1930. o. 261S~r.lnmcsJranz likens the problem to having the position and momentum of the particle marked on the two different faces of a oroiector slide. Focussine the
..
focus more precisely on one face causes theother to become increasingly blurred, i.e., trying t o reduce Ap (or AY)leads automatically to an increase in Ay (or Ap), and there is nothing that we can do with the projector controls to bring bothp and y into sharp focus a t the same time. Present day teaching situations rarely provide either the projectors or the thick slides of Jeans' day, hut the ubiquitous overhead projector can be easily substituted. The large depth of field of the OHP makes it necessary to separate the two faces even more drastically than on a thick projector slide. However, this separation is easily achieved by separating two sheets of Perspexaof suitable surface dimensions (say 10 cm X 15 cm) by (wooden) spacers a t a distance of approximately 8 cm, as shown in the figure (a). "POSITION" and "y" are written on the top sheet (a felt tip pen is suitable) and "MOMENTUM and "p" on the lower one. I also draw a straight line on the lower (momentum) sheet to represent the direction of travel, and hence the velocity, of the particle and a dot on the upper (position) sheet,vertically over the line (this is best done with the apparatus in position on the OHP), to represent the position of the particle. Parts ( b ) ,( e ) and ( d ) of the Figure show the projected image when the OHP is focussed on the top sheet, between the sheets, and on the lower sheet, respectively. Two cautionary notes: (1) do not make the distance hetween the sheets too large or the OHP lens will not have sufficient upward travel to bring the top sheet into focus, nor enough downward travel t o focus on the lower sheet; and (2) as with all models and analogies it is important to stress the illustrative nature of the demonstration to prevent some of the students from getting the impression that the Uncertainty Principle consists of two Perspex sheets held apart by wooden spacers!
Ronald C. C m e r Rhodes University Grahsmstown, 6140, Re~ublicof Souih Africa
300
Journal of Chemical Education
