For scattering under the influence of the Coulomb forcethe angle of scattering is related to the impact parameter b illustrated at left. Under the assumption that the target recoil is negligible, the change in momentum associated with the scattering is.
One way to obtain an expression for the change in momentum is to use the concept of impulse of force and the symmetry of the scattering geometry. Only the impulse component along the symmetry axis of the hyperbola will produce a net momentum change.
Conservation of angular momentum can be used to advantage in evaluating the impulse integral. Here we have used the expression for the angular momentum of a particle and the fact that it can be expressed as the product of mass, radius, and velocity perpendicular to the radius at any point on the hyperbolic path. Substitution gives. Extending the entrance and exit paths of the scattering trajectory to infinity gives the limits on the angle:. The two forms above can be shown to be equivalent using the half-angle identities.
In this expression k is Coulomb's constant, e the electron charge and KE is the kinetic energy of the projectile particle. Impact Parameter for Nuclear Scattering Click for detail. Under the assumption that the target recoil is negligible, the change in momentum associated with the scattering is where the magnitudes of the initial and final momenta are the same.
Index Rutherford concepts.Pharmacokinetics, sometimes described as what the body does to a drug, refers to the movement of drug into, through, and out of the body—the time course of its absorptionbioavailabilitydistributionmetabolismand excretion. Pharmacodynamicsdescribed as what a drug does to the body, involves receptor binding, postreceptor effects, and chemical interactions.
Formulas relating these processes summarize the pharmacokinetic behavior of most drugs see table Formulas Defining Basic Pharmacokinetic Parameters. Some patient-related factors eg, renal function, genetic makeup, sex, age can be used to predict the pharmacokinetic parameters in populations. For example, the half-life of some drugs, especially those that require both metabolism and excretion, may be remarkably long in the elderly see Figure: Comparison of pharmacokinetic outcomes for diazepam in a younger man A and an older man B.
In fact, physiologic changes with aging affect many aspects of pharmacokinetics see Pharmacokinetics in Older Adults and see Pharmacokinetics in Children. Other factors are related to individual physiology. The effects of some individual factors eg, renal failure, obesity, hepatic failure, dehydration can be reasonably predicted, but other factors are idiosyncratic and thus have unpredictable effects.
This approach is frequently inadequate because it can delay optimal response or result in adverse effects. Knowledge of pharmacokinetic principles helps prescribers adjust dosage more accurately and rapidly.
Overview of Pharmacokinetics
Application of pharmacokinetic principles to individualize pharmacotherapy is termed therapeutic drug monitoring. Diazepam is metabolized in the liver to desmethyldiazepam through P enzymes. Desmethyldiazepam is an active sedative, which is excreted by the kidneys. Elimination half-life is inversely proportional to the terminal slopes of the curves; flat slopes correspond to long half-lives. Clinical Pharmacology and Therapeutics —, From developing new therapies that treat and prevent disease to helping people in need, we are committed to improving health and well-being around the world.
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Comparison of pharmacokinetic outcomes for diazepam in a younger man A and an older man B Diazepam is metabolized in the liver to desmethyldiazepam through P enzymes. Drug Name Select Trade diazepam. Was This Page Helpful? Yes No.Impedance parameters or Z-parameters the elements of an impedance matrix or Z-matrix are properties used in electrical engineeringelectronic engineeringand communication systems engineering to describe the electrical behavior of linear electrical networks.
They are also used to describe the small-signal linearized response of non-linear networks. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters Y-parameters H-parametersT-parameters or ABCD-parameters. Z-parameters are also known as open-circuit impedance parameters as they are calculated under open circuit conditions.
A Z-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports. A port in this context is a pair of electrical terminals carrying equal and opposite currents into and out-of the network, and having a particular voltage between them.
The Z-matrix gives no information about the behaviour of the network when the currents at any port are not balanced in this way should this be possiblenor does it give any information about the voltage between terminals not belonging to the same port. Typically, it is intended that each external connection to the network is between the terminals of just one port, so that these limitations are appropriate.
For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer n ranging from 1 to Nwhere N is the total number of ports. For all ports the voltages may be defined in terms of the Z-parameter matrix and the currents by the following matrix equation:. In general the elements of the Z-parameter matrix are complex numbers and functions of frequency.
For a one-port network, the Z-matrix reduces to a single element, being the ordinary impedance measured between the two terminals. The Z-parameters are also known as the open circuit parameters because they are measured or calculated by applying current to one port and determining the resulting voltages at all the ports while the undriven ports are terminated into open circuits.
The Z-parameter matrix for the two-port network is probably the most common. In this case the relationship between the port currents, port voltages and the Z-parameter matrix is given by:.
The Z-parameters of a network are related to its S-parameters by . In these expressions the matrices represented by the bracketed factors commute and so, as shown above, may be written in either order.
The two-port S-parameters may be obtained from the equivalent two-port Z-parameters by means of the following expressions .
Conversion from Y-parameters to Z-parameters is much simpler, as the Z-parameter matrix is just the inverse of the Y-parameter matrix. For a two-port:. From Wikipedia, the free encyclopedia. Pozar Microwave Engineering. Pozar, op. Electromagnetics, microwave circuit and antenna design for communications engineering.
Impact Parameter for Nuclear Scattering
Artech House. Whinnery; Theodore Van Duzer Fields and Waves in Communication Electronics. Categories : Electrical parameters Two-port networks Transfer functions. Namespaces Article Talk.
Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version.In Ernest Rutherford's laboratory, Hans Geiger and Ernest Marsden a 20 yr old undergraduate student carried out experiments to study the scattering of alpha particles by thin metal foils.
This led Rutherford to deduce that the positive charge in an atom is concentrated into a small compact nucleus. During the period in a table-top apparatus, they bombarded the foils with high energy alpha particles and observed the number of scattered alpha particles as a function of angle. Based on the Thomson model of the atom, all of the alpha particles should have been found within a small fraction of a degree from the beam, but Geiger and Marsden found a few scattered alphas at angles over degrees from the beam.
Rutherford's remark "It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a inch shell at a piece of tissue paper and it came back and hit you. Rutherford worked out a detailed formula for the scattering Rutherford formulawhich matched the Geiger-Marsden data to high precision. The source used in the Rutherford experiments was purifed radium contained in a thin-walled 1-mm diameter glass tube.
The source strength was about 0. The alpha particles were allowed to pass through a small diaphragm and were directed toward a thin foil target. The detector was a small 10 -6 m 2 zinc sulfide screen mounted a few centimeters away from the target. Geiger and Marsden showed that the number of scattered alpha particles as a function of scattering angle was consistent with a small, concentrated positive nucleus.
To angles above degrees, the nucleus appeared as a point positive charge, so this data did not measure the nuclear size. When the scattering departed from that predicted from Coulomb's lawit could be inferred that another force was coming into play and you could claim to have "hit" the nucleus.
At degrees, they still hadn't hit it. Since they had used the most energetic alpha particles at their disposal, 7. This led to a famous remark by Rutherford to his graduate students "There is no money for apparatus.
Regardless of the nature of the force in an elastic collisionto get a scattering angle greater than 90 degrees, the target must be more massive than the projectile. Besides the masses of the target and projectile, the scattering angle depends upon the force and upon the impact parameter.
The impact parameter is the perpendicular distance to the closest approach if the projectile were undeflected. Determining the closest approach to the nucleus amounts to calculating the minimum distance for the hyperbolic orbit which is produced by the coulomb repulsive force. The expression for the closest approach as a function of the impact parameter b is given by: Which has a limit for back-scattering which is just determined by setting the initial kinetic energy equal to the final potential energy.
This corresponds to stopping the projectile and sending it backward, so at its closest approach, all the energy is in electric potential energy. The closest approach for the trajectory described above is then. Rutherford scattering was the first method used to measure the size of nuclei. More precise measurements are made with electron scatteringand it was discovered that the density of nuclei is approximately constant.
This has made possible the modeling of nuclear radii from just their mass numbers.It is often referred to in nuclear physics see Rutherford scattering and in classical mechanics.
The simplest example illustrating the use of the impact parameter is in the case of scattering from a sphere. In high-energy nuclear physics — specifically, in colliding-beam experiments — collisions may be classified according to their impact parameter.
Because the color force has an extremely short range, it cannot couple quarks that are separated by much more than one nucleon's radius; hence, strong interactions are suppressed in peripheral and ultraperipheral collisions. This means that final-state particle multiplicity is typically greatest in the most central collisions, due to the partons involved having the greatest probability of interacting in some way.
This has led to charged particle multiplicity being used as a common measure of collision centrality charged particles are much easier to detect than uncharged particles. Because strong interactions are effectively impossible in ultraperipheral collisions UPCsthey may be used to study electromagnetic interactions — i. Because UPCs typically produce only two- to four final-state particles, they are also relatively "clean" when compared to central collisions, which may produce hundreds of particles per event.
From Wikipedia, the free encyclopedia. Categories : Classical mechanics. Hidden categories: All stub articles Physics stubs. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file.
Download as PDF Printable version. This physics -related article is a stub. You can help Wikipedia by expanding it.For example, count to three while lowering a weight, hold, then count to three while raising it to the starting position. Pay attention to your breathing during your workouts.
Keep challenging muscles by slowly increasing weight or resistance. The right weight for you differs depending on the exercise. Choose a weight that tires the targeted muscle or muscles by the last two repetitions while still allowing you to maintain good form. If you can't do the last two reps, choose a lighter weight. When it feels too easy to complete add weight (roughly 1 to 2 pounds for arms, 2 to 5 pounds for legs), or add another set of repetitions to your workout (up to three sets).
If you add weight, remember that you should be able to do all the repetitions with good form and the targeted muscles should feel tired by the last two. Stick with your routine working all the major muscles of your body two or three times a week is ideal. You can choose to do one full-body strength workout two or three times a week, or you may break your strength workout into upper- and lower-body components.
In that case, be sure you perform each component two or three times a week. Give muscles time off.
Strength training causes tiny tears in muscle tissue. These tears aren't harmful, but they are important: muscles grow stronger as the tears knit up. Always give your muscles at least 48 hours to recover before your next strength training session.
Easy exercises for couch potatoes Improve your balance by strengthening your core Daily Health Tip Build muscle strength Building muscle isn't just for individuals into fitness as a hobby. Our FREE E-mail Newsletter In each issue of HEALTHbeat: Get trusted advice from the doctors at Harvard Medical School Learn tips for living a healthy lifestyle Stay up-to-date on the latest developments in health Receive special offers on health books and reports Plus, receive your FREE Bonus Report, "101 Tips for Tip-Top Health" E-mail Address First Name (Optional) The Harvard Medical School 6-Week Plan for Healthy Eating (Print - Free U.
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