THE SCATTERING OF HYDROGEN IONS IN HYDROGEN AND WATER

52 Pages·02.74 MB·English

by  FONTANA, C. M

DOCTORAL DISSERTATION SERIES
_
Uje Scattering of Hydrogen Io n s
TITLE
in Hydrogen dnd Water
_
C.M. T o n ta n d
AUTHOR DATE
A u g . 1 9 4 - 2
___
Tbmsiflvanid. Sfdle College.
UNIVERSITY,
M b sss
DEGREE PUBLICATION NO.
^ UNIVERSITY MICROFILMS
A N N A R B O R - M I C H I G A N
The Pennsylvania State College
The Graduate School
Department of Chemistry
The Scattering of Hydrogen Ions
in Hydrogen and water
A Dissertation
by
C. M. Fontana
Submitted in partial fulfillment
of the req.uirem.ents
for the degree' of
Doctor of Philosophy
August, 1942
/
/
Approved • /
Depthof Chemistry
Head of the Dept'
Acknowledgment
The author wishes to express to Professor J. H. Simons
a sincere appreciation for his direction, constant
encouragement and numerous suggestions throughout the
course of this work.
The author is indebted to Dr. A. S. Russell for his
wholehearted cooperation in the earlier work through which
a great portion of the experience necessary for the
construction of the apparatus used in this research was
gained.
Acknowledgment is due also the Messrs. H. T. Francis,
S. R. Jackson, L. G-. Unger and E. E. Muschlitz for their
unreserved cooperation and assistance in the construction
and operation of the present apparatus.
TABLE OF CONTENTS
Part I - Introduction page 1
Historical 2
The Scattering Process 3
The Statistical Nature of Scattering
Experiments 6
Discussion of the Approximations In the
Scattering Laws 8
+ _i_
Part II - Scattering Experiments with H and Hg
in Hydrogen 12
Discussion of Data on in Hydrogen 14
Discussion of Data on H,^ in Hydrogen 20
o
Part III - Neutralization and Scattering 25
Separation of Scattering and Neutralization
Cross Sections 27
Discussion of Besults ( H~ in II ) 30
^ 2
Part 17 - Scattering Experiments with Water and
General Discussion 37
Summary 45
Bibliography 48
Part I - INTRODUCTION
Scattering experiments have been the source of some
of the most significant information concerning the nature
of matter. Thus the scattering experiments of Rutherford
employing fast alpha particles have led to the modern
concepts of the constitution of the atom. Later the
scattering experiments with X-rays and with electrons have
not only revealed structural details of materials studied
but also have established the fundamental wave nature of
material particles. This in turn in the case of electron
diffraction has been one of the most recent means of
elucidating structural details of simple molecules.
It is not surprising then that scattering experiments
can be used again in the investigation of those relatively
weak force fields existing between molecules and ions.
In these investigations relatively slow ions must be used
because of the magnitude of the force fields involved.
The object of this research is the investigation of
the force fields between ions and simple molecules,
particularly between protons and molecules, by means of
beams of slow positive ions.
2
Historical.-
The problems associated with the passage of charged
particles through gases at low pressures arose first
purely as technical problems in positive ray analysis by
means of the mass spectrograph. Most of the early work
was done with fast ions as for example that of Thomson^-1-)
who passed protons through hydrogen gas at energies of
5,000 to 25,000 electron volts.
The first work with the scattering of slow massive
(2}
ions was by Aich' ' who determined a single point of the
cross section curve at 17 volts and obtained a scattering
radius of 1.35X10 cm. corresponding to a cross section
of 20.4 for H* in H2.
In 1930 Holzer^*^ reported measurements on the cross
section for scattering of H +‘, H^ , and K,£ in Hg over a
range of velocity from 50 to 300 volts. A little later
Ramsauer, Kollath and Lilienthal obtained results for
the scattering of protons in Hg, Ng, He, and A in the
range 25 to 2,500 vo^ts. All these early measurements
show large inconsistencies (as much as 100^ or more)
especially at low velocities (less than 50 volts) where
attractive forces determine the scattering.
The recent scattering measurements of Russell, Fontana
(5)
and Simons' indicated that precise scattering measure­
ments can be obtained at low velocities and it was this
indication that prompted the building of a considerably
improved apparatus for obtaining more precise measurements
especially at low velocities and for the separation of
effects other than scattering such as neutralization of
the ion beam. The description of this apparatus forms
the subject matter of a thesis by S. R. Jackson^6^ and
no additional description will be necessary here.
The Scattering Process.-
An approximate expression for the angle of scattering
as a function of potential law and distance of closest
approach, r6 , can be derived in the following manner:
Consider a particle of mass m moving along the x
axis as in figure 1, and passing near another particle
considered to be of infinite mass, to which it is attracted
according to a potential function
v = - E— . .(i-i)
rn
(Figure 1)
For small scattering angles the force in the z direction
is given by the expression
_ n ,K cos B. (1-2)
Fz ~ r (n+1)
The z component of velocity after scattering will be
4cO
__ n Kyb \ - ~ r ---
z = LLyf)— J +
— -O
where r*+v*tzand v is the original velocity of the
particle in the x direction.
The solution of this integral is
2K T 1*3*5* * * * (n-1) . 777
v„ —
z mvr 8-'4 - 6 (n) — J for n eTe».
_ 2E r ...... (n-l)l
*-Ln - {n) J ±0* * °dd>
mvr_
— ^KC (1—4)
mvr^ x 1
where C is a constant depending only on the value-of n
in the potential law. The general expression for G
including non-integral values of n is
r _ 1/WrUnti)
c - rliii) ■
the symbol V representing the gamiaa function.
The scattering angle j> is given by
tan — 2Ko __ EC (1-5)
v mvarV
where V/ is the initial kinetic energy of the scattered
particle.
(7)
This equation was first derived by Zwicky ana
was reproduced here to show the approximations involved
in its derivation.
It is now necessary to consider trie effect of finite
and comparable masses. In this case W must be replaced
by the internal energy, E, which is related to V by
E = (1-6)
where u is the reduced mass, SnELi— , and m, is the mass
m,-+-mA
of the scattered particle. The angle is now the relative
angle of scattering, i.e. the angle of scattering in a
moving non-rotating system of coordinates with origin
at the scatterer. The relation between tan{> and tan^
where 0 is the angle of scattering on a stationary
system of coordinates can be arrived at through considera­
tion of conservation of momentum and energy in the system.
With reference to figure 2, the following equations
express the conservation laws:
m , v* — m,v, cos <f> +- m 1vXi
m zv2t =. m,v, sin f
§m,v/ = im, v,2- -+•
tWj. Vz.
(Figure 2)
The relative angle O is given by
tan6 = Ia±l£- = --------------- f tiis L iaa (1.7)
Vx, -TXa oos+ ^ m, / m .-mil, . oosU
T mt\m, co ,xsin^ /
For small scattering angles and m, comparable to m r
this reduces to
tan 9 = tan = tan (1.8)
which is the desired relationship.
Substitution of the above relations for E and tan d in
tan Q r
gives the equation
K C .
r *; _ _ Tf (1-10)
W r*
tanHv')
whieh is identical with equation (1-5).
It may therefore be concluded that equation (1-10)
or (1-5) is approximately correct for small angles of
scattering and for particles of comparable mass.
The Statistical Mature of Scattering Experiments.-
In a scattering experiment a fine beam of ions is
passed coaxially through a cylinder containing gas at
low pressure as represented in figure 3. One measures
the fraction of current, R, which passes through the
scattering chamber. With reference to the figure it is
clear that a particle is counted as scattered if it is
deflected through some angle greater than a limiting
small angle<f) which depends on the position along the
cylinder at which scattering takes place.
j
(Figure 3)
Let I =; the intensity of the beam at any distance x
from the entrance of the scattering chamber