MARCH,1945
Valence Angle of the Tetrahedral Carbon Atom W. E. BRITTIN University of Colorado,Boulder, Colomdo
v
ARIOUS methods of calculating the valence bond angle ~n . the tetrahedral carbon atom have been proposed.'. 2. Some of the geometric methods, although not essentially difficult, are somewhat lengthy and involved. The following vector method has pedagogic appeal because of the natural way vectors lend themselves to the representation of directed quantities, and because of the simplicity of the elementary vector algebra used. Represent the valence bond directions by four unit vectors, ul, u2, ua, u4 (see figure). Symmetry demands that the vector sum of the four vectors vanish: By definition the scalar product of two unit vectors is equal to the cosine of the angle between them. Thus, cos a, i Z
j
cos 0 = 1, i = j
, j
=1
.4
(2)
where a is the angle between the valence bonds. Take the scalar product of one of the unit vectors, ul say, and equation (I),
1
UNITVECTORSUSED TO REPRESENT THE VALENCEBONDDIRECTIONS
Then using relations (2) there results l+Scosa=O
(5)
ties of the scalar product, the following argument may be used: In order that the sum of the four vectors be zero, the sum of the components in any direction must be zero. Taking the sum of the z-components (see figure), one obtains, (7)
30-1=0
But For students who have no knowledge of the proper-
' GOMRFRT. G . L., J. CIIEM.Encc.. 18,336 (1941). DORE.'A'. 11.. tbid., l9,2d (194'2). W'EA~~P P.~F.,iLid., I L L ,19.35 (1942).
hence ar = 7 / 2
+ sin-'
('Is)
= 109'28'
16'
(9)
OUT OF THE EDITOR'S BASKET (Continued from page 139) Asiatic nations with conscription should be made generally available to the citizens of this country before the matter comes to a vote, and while the arguments of the military departments should be given most careful consideration, the final decision must reflect the mature thought of the civilians of the United States. That is an American tradition which must be maintlinea "
In a petition on this subject which the Council sent to the Presidentof the United States is the following
paragraph which we think important enough to quote: "Should not compulsory military training be considered as one part of total national defense? A modern army needs more than reserves. It requires continuous research on the development of tools of warfare, maintained stockpiles of essential raw materials, and adequate industrial producing capacity in a stand-by or easily convertible condition to provide the immense quantities of goods needed in combat. If we are t o embark upon a program of manpower preparation for total war, should not all these problems be considered together?"
