To investigate these dynamics, we measure how the number of molecules N M and the number of unbound atoms N A change as a function of time. We measure N A by using standard absorption imaging. However, prior to the imaging we first remove all Feshbach molecules from the gas. The laser pulse has a duration of 0. For this we use again absorption imaging. The Feshbach molecules are so weakly bound that the imaging laser resonantly dissociates them quickly into two cold atoms which are subsequently detected via absorption imaging Besides this, N A also exhibits a slow, steady increase which we attribute to a background heating of the gas, e.
It can be completely explained by inelastic collisions between molecules as previously investigated in ref. In principle, collisional dissociation in our experiment can be driven either by atom—molecule collisions or by molecule—molecule collisions. In a simple physical picture, the suppression of the atom—dimer dissociation is due to the Pauli principle acting on the outgoing channel, which involves two identical fermionic atoms 31 , Therefore, to first order, we only need to consider dissociation into two atoms.
12.5 Collision Theory
The evolution of the density n A of unbound atoms is then given by the rate equation,. Here, n M is the molecule density and C 2 R 2 are the rate constants of molecule dissociation association. A spatial integration of Eq. Furthermore, in Eq. By fitting Eq. Next, we investigate how the reaction rates depend on temperature. This result can be compared to a prediction based on statistical mechanics 23 ,.
The agreement between experiment and theory is quite good. Temperature dependence of the equilibrium state and temperature evolution. The error bars denote the s. The continuous line is a calculation without any free parameters for details see section "Temperature dependence". In addition, it excites small collective breathing mode oscillations, see the red line as a guide to the eye.
The temperature scale applies to the non-oscillatory part of the data. The mean cloud size which is obtained by averaging over one oscillation red circles in Fig. This might be at first surprising since one might expect the endothermic dissociation to considerably lower the temperature again. Therefore only a small amount of the injected heat is consumed for the dissociation, corresponding to a small amount of cooling.
Moreover, this residual cooling is almost canceled by the background heating. From our results in Fig. The solid curve in Fig. Finally, we investigate the influence of the interaction strength between the particles on the reaction dynamics. For this, we tune the scattering lengths with the help of the magnetic B-field. However, this has negligible influence on the dynamics of the dissociation, which we have checked with a numerical calculation. Already from the data shown in Fig. From fits to these and additional measurements we extract R 2 a and C 2 a for various scattering lengths and plot the results on a double logarithmic scale in Fig.
Dependence of the reaction rate constants on the scattering length. The continuous lines are fits based on Eq. The majority of the data can be found in a band orange area around the fit curve.
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To compensate the influence of the temperature, we use Eq. The blue continuous line is the theoretical prediction of Eq. The association three-body recombination process characterized by the rate constant R 2 has been extensively discussed for various Efimovian systems 34 — 36 , where it depends on the three-body parameter, and for non-Efimovian Fermi—Fermi mixtures, where it is suppressed in the low-energy limit 31 , In Fig.
Our results show quite good agreement with the expected power law dependence within the error bars. In order to compensate this temperature change, we use Eq. The resulting rate constant C 2 increases by more than one order of magnitude in the tuning range and agrees reasonably with the theoretical prediction without any free parameter ,.
As far as we know there is no direct theoretical prediction for this number. The large discrepancy between the theoretical and experimental value needs to be investigated in future studies.
It may be due to an atom dimer attraction in the p -wave channel see supplemental material of ref. In conclusion, we have investigated the collisional dissociation of ultracold molecules in a single reaction channel which is characterized by the precisely defined quantum states of the involved atoms and molecules.
This allows us to determine reaction rate constants, in particular for the collisional dissociation of two molecules. Furthermore, we find a strong temperature dependence of this rate which is consistent with the well known Arrhenius equation. For the future, we plan to extend the current work to study the dynamics of chemical reactions in a regime, where Fermi and Bose statistics play an important role. The scattering length a as a function of the B-field is taken from ref.
The excited molecular state decays within a few ns either into two unbound atoms which quickly leave the trap or into deeply bound Li 2 molecules which are invisible for our detection. Besides molecule excitation, the pulse leads to photoassociation of unbound atoms.
Molecules must collide before they can react
This reduces the number of free atoms and leads to an overestimation of the molecule number. The authors thank C. Collision theory explains why most reaction rates increase as concentrations increase. With an increase in the concentration of any reacting substance, the chances for collisions between molecules are increased because there are more molecules per unit of volume. More collisions mean a faster reaction rate, assuming the energy of the collisions is adequate. The kinetic energy of reactant molecules plays an important role in a reaction because the energy necessary to form a product is provided by a collision of a reactant molecule with another reactant molecule.
In single-reactant reactions, activation energy may be provided by a collision of the reactant molecule with the wall of the reaction vessel or with molecules of an inert contaminant. If the activation energy is much larger than the average kinetic energy of the molecules, the reaction will occur slowly: Only a few fast-moving molecules will have enough energy to react. If the activation energy is much smaller than the average kinetic energy of the molecules, the fraction of molecules possessing the necessary kinetic energy will be large; most collisions between molecules will result in reaction, and the reaction will occur rapidly.
This lost energy is transferred to other molecules, giving them enough energy to reach the transition state. Both postulates of the collision theory of reaction rates are accommodated in the Arrhenius equation. In such cases, no reaction occurs. At the other extreme, the system has so much energy that every collision with the correct orientation can overcome the activation barrier, causing the reaction to proceed. In such cases, the reaction is nearly instantaneous. The Arrhenius equation describes quantitatively much of what we have already discussed about reaction rates. For two reactions at the same temperature, the reaction with the higher activation energy has the lower rate constant and the slower rate.
An increase in temperature has the same effect as a decrease in activation energy. The variation of the rate constant with temperature for the decomposition of HI g to H 2 g and I 2 g is given here. What is the activation energy for the reaction? The Arrhenius equation:. For this example, we select the first entry and the last entry:. This method is very effective, especially when a limited number of temperature-dependent rate constants are available for the reaction of interest.
These reactant collisions must be of proper orientation and sufficient energy in order to result in product formation. Collision theory provides a simple but effective explanation for the effect of many experimental parameters on reaction rates. Chemical reactions occur when reactants collide. What are two factors that may prevent a collision from producing a chemical reaction?
When every collision between reactants leads to a reaction, what determines the rate at which the reaction occurs? What is the activation energy of a reaction, and how is this energy related to the activated complex of the reaction? Describe how graphical methods can be used to determine the activation energy of a reaction from a series of data that includes the rate of reaction at varying temperatures.
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How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate. Determine the frequency factor for the reaction. Determine the activation energy for this decomposition. An elevated level of the enzyme alkaline phosphatase ALP in the serum is an indication of possible liver or bone disorder.
The level of serum ALP is so low that it is very difficult to measure directly. However, ALP catalyzes a number of reactions, and its relative concentration can be determined by measuring the rate of one of these reactions under controlled conditions. Control of temperature during the test is very important; the rate of the reaction increases 1. Out of stock. Get In-Stock Alert. Delivery not available. Pickup not available. Atomic and Molecular Collision Theory About This Item We aim to show you accurate product information.
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