DONNABOGNER
Hutchinson Senior High S e h l
Hutchinson, KS 6 7 5 0 1
The Significance of Arrows in Orbital Diagrams
Clark S. Burdman
Manhasset H@ S c h d
Manhasset, NY 1 1 0 3 0
Most introductory college chemistry texts (1-4) and many
high school texts (5, 6 ) discuss orbital diagrams for representing electron configurations in atoms or molecules. In
this notation, an orbital is represented by a 0,( ), 0,or and electrons are usually represented by arrows pointing up
or down.
An electron behaves as if i t were spinning on its axis. An
up arrow (t) represents an electron spinning in one direction, and a down arrow (4) represents an electronspinning in
the opposite direction. T o a student first studying chemistry
it might seem arbitrary to represent an electron's spin by up
or down arrows as opposed to saying clockwise or counterclockwise spin. I have not seen any introductory text that
explains the meaning of the direction of arrows used to
represent electron spin.
In order t o show the significance, draw a circle on a piece
of translucent Daver. and draw arrows to show the direction
of an electrous&nning on its axis. The following diagram
illustrates an electron spinning counterclockwise on its axis
as viewed from above.
0
If the paper is lifted up and viewed from below, the same
electron appears to hespinniugclockwise. Thus, the electron
can he spinning counterclockwise or clockwise depending on
the observer's frame of reference. The terms of clockwise or
320
Journal of Chemical Education
counterclockwise, therefore, are not sufficient for indicating
the direction of an electron's spin.
Spinning objects possess angular momentum. Angular
momentum is a measure of an object's ability to continue in
motion a t a constant speed or angular velocity about an axis
of rotation. I t is a vector quantity. The direction of the
a right-hand rule (7),
angular lnomentum vector is given
the fingers of the right hand in the direction of motion
and the extended
of the right hand points in the
direction of the angular momentum vector.
When this right-hand rule is applied to the above diagram
as viewed from above, the thumb of the right hand pointsup.
When the paper is lifted and viewed from below and the
right-hand rule is applied, the thumb of the right hand again
points up, Thus, the direction of the spinning electron,s
angular momentum vector is always pointing
the
ceiling. We can unambiguously represent this electron's spin
with an and say its
angular momentum is
A
similar argument can he used if the direction of the electrou,s spin is clockwise as viewed from above. Thus, the
arrows are related to the direction of an electron's spin angular momentum vector (8),
(11 Brown,Theodore L.; LeMay, H. E. "Chemistry: the Central Science", 3rd ed.; Prentice-Hell: EnglewMdCliff%,NJ 1986: (1159.
(21 Masterton. William L.: Slowinski. Emil J. '"ChemicalPrineipiealvithQuelitstive Analysis", 4th ed.; Ssunders: Philadelphia, 1978: p 137.
(3) Nebergall. William H.: Schmidt, Frederie C.: Holtzclaw. HenryF."Colleg. Chemistry
with Qualitative Analysis," 5th ed.: Health: Lexington. MA, 1976: p 105.
(4) Mortimer, Charles E. "Chemistry", 5th ed.; Wadsworth: Belmont. 1983; p98.
( 5 ) Smoot, Robert C.: Price, Jsck S.; Smith, Richard G. "Chemistry A Modem Course':
Merriil: Columbus. OH, 1983; p 165.
(61 Twn, Ernest R.:Ellis,Goorge L. "Foundationsof Chemistry, 2 n d d . ; Hoit,Rinehart
and Winston: New York, 1973; p 2W.
(71 White. Harvey E. "Modern College Physid'. 6th d . ; Van Noatrand Reinhold: New
York, 1972; p 220.
(8) Ret 7, Chap 45, "Spinning Eleetmns".