The course gives the overview of the physical chemistry of collisions. First of all, the concept of the collision cross section is presented. Then the collision is treated in a classical manner. The relation between the orbit of the colliding particle and the interaction potential is expalined. The differential cross section of the Rutherford scattering is derived. After that we move on to the quantum mechanics. It is expalined that the collision is described by the unbound solution of the wave equation. Then, the manner of obtaining the collision cross section is presented. Finally, the Bethe approximation, which is widely used, is discussed.
The aim of this course is getting the recipe for understanding reactions from the point of view of mechanics.
By the end of this course students will be able to understand that the chemical reaction is considered a kind of collision processes and will get the method of discussing the reaction in both of classcal manner and quantal manner.
collision cross section, differential cross section, elastic and inelastic collision, interactionpotential, orbit, two-body problem, bound and unbound solution, scattering amplitude, Bethe approximation
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
The classes start from understanding the chemical reaction from the view point of atomic and molecular collision. Next, the physical chemistry of collisions is discussed from the classical points of view, and finally, from the quantal points of view.
|Course schedule||Required learning|
|Class 1||The chemical reaction and atomic and molecular collision||Understand the relation between the chemical reaction and atomic and molecular collision.|
|Class 2||The atomic and molecular collision(1)-the energy conservation law and collision||Classify collisions in terms of the energy conservation law|
|Class 3||The atomic and molecular collision(2)-the reaction cross section and reaction rate constant||Explain the relation between the reaction cross section and reaction rate constant.|
|Class 4||The atomic and molecular collision(3)-the differential crsoss section and interaction between two particles||Understand the relation between the differential cross section and two-body interaction.|
|Class 5||The collision from the classical points of view(1)-the potential energy and orbit||Understand that the collision orbit is governed by the intermolecular potential.|
|Class 6||The collision from the classical points of view(2)-Collision from the classical point of view and the collision cross section in the classical mechanics||Understand the collision under the centrifugal coulomb potential from the classical point of view and obtain its collision cross section.|
|Class 7||The two-body problem in the quantum mechanics(the separation of the motion of the center of mass and the relative motion)||Understand that the wave equation of the total system is divided into the part of the motion of the center of mass and the part of the relative motion.|
|Class 8||The two-body problem in the quantum mechanics(the separetion of the angular coordinates and radial coordinate)||Understand that the wave equation of the relative motion is divided into angular and radial parts.|
|Class 9||The two-body problem in the quantum mechanics(bound and unbound states)||Understand that the wave equstion has two kinds of solutions, i.e. one is bound solution and the other is unbound solution.|
|Class 10||The probability current density||Understand the concept of the probability current density.|
|Class 11||The quantal way of calculating the collision cross section(the expansion of the total wave function by the eigenfunctions of target atoms)||Understand how to expand the wave function of the total system by the eigenfunctions of target atoms.|
|Class 12||The quantal way of calculating the collision cross section(the asymptotic form of the wave function at the infinite distance)||Expalin the asymptotic form of the wave function of the collisional system at the infinite distance.|
|Class 13||The quantal way of calculating the collision cross section(calculation of the differential cross section)||Obtain the differentail cross section based upon the 11th class and 12th class.|
|Class 14||Summary||Briefly summarize individual subjects learned in whole course.|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Home-made textbook is distributed.
B. H. Bransden and C. J. Joachain, Physics of atoms and molecules, 2nd Edition, Pearson Education
Students are assessed on understanding of basic concepts and applicability of them.
Homework assignments 25%
Final examination 75%
We recommend that students have successfully completed Introductory Chemical Kinetics(CHM.C301 ) and Exercise in Introductory Chemical Kinetics(CHM.C303).
Masashi Kitajima: mkitajim[at]chem.titech.ac.jp
Contact by email in advance to schedule an appointment.
Masashi Kitajima(West Building 4, Room 503)