Half-life and rate

Aii radioactive decay processes foiiow first-order kinetics. What does this mean What happens to the rate of radioactive decay as the number of nuciides is haived Write the first-order rate law and the integrated first-order rate law. Define the terms in each equation. What is the half-life equation for radioactive decay processes How does the half-life depend on how many nuclides are present Are the half-life and rate constant k directly related or inversely related ... 

Knowledge Required (1) The knowledge that radioactive decay is a first-order process. (2) The integrated form of the first-order rate equation. (3) The relationship between half-life and rate constant... 

Equation 10.18 suggests that the loading dose is determined by the proposed infusion rate and the patient s elimination half life and rate constant. 

It is clear from Eqs 11.36 and 11.37 and Table 11.2 that dmg fluctuation, just as for dmg accumulation, is simply a function of dosing interval and the elimination half life or elimination rate constant of a dmg. Since the elimination half life and rate constant are constant for a particular dmg administered to an individual patient, fluctuation is influenced only by the dosing interval. It should be clear from Table 11.2 that the more frequent the dosing of a dmg, the smaller is the... 

Find k by substituting into the equation relating half-life and rate constant for a first-order reaction. ... 

Toluene, volatile nitrites, and anesthetics, like other substances of abuse such as cocaine, nicotine, and heroin, are characterized by rapid absorption, rapid entry into the brain, high bioavailability, a short half-life, and a rapid rate of metabolism and clearance (Gerasimov et al. 2002 Pontieri et al. 1996, 1998). Because these pharmacokinetic parameters are associated with the ability of addictive substances to induce positive reinforcing effects, it appears that the pharmacokinetic features of inhalants contribute to their high abuse liability among susceptible individuals. 

In a study of pregnant rats that were exposed to radiolabeled methyl parathion by single dermal application, half-life elimination rate constants for various tissues ranged from 0.04 to 0.07 hour, highest values noted in plasma, kidneys, and fetus. Of the applied radioactivity, 14% was recovered in the urine in the first hour postapplication. By the end of the 96-hour study, 91% of the applied dose had been recovered in the urine. Fecal excretion accounted for only 3% of the administered dose (Abu-Qare et al. 2000). 

Because p-blockers decrease blood pressure and heart rate, they should be started at low doses to increase tolerability. Propranolol is hepatically metabolized, and its half-life and pharmacologic effects are prolonged in portal hypertension. A reasonable starting dose of propranolol is 10 mg two to three times daily. 

The analysis of absorption data in humans has moved away from the more traditional modeling and data fitting techniques [35]. Absorption processes are now more often characterized by a mean absorption (or input) time (i.e., the average amount of time that the drug molecules spend at the absorption site) or by a process called deconvolution. The former analysis results in a single value (similar to absorption half-life) and the latter results in a profile of the absorption process as a function of time (e.g., absorption rate or cumulative amount absorbed vs. time). These approaches offer additional ways of interpreting the absorption process. 

Given the rate constant or half-life and the initial concentration, calculate the concentration at some time in the future. 

Statement (d) is incorrect it implies a constant rate during the first half-life. The rate of a first-order reaction actually decreases as time passes and reactant is consumed. 

After the pool sizes are determined, the first-order rate constant (k), half-life, and MRT can be determined using the equations ... 

Determine the rate equation for the decomposition of tetrahydrofuran with the aid of the tabulated data of initial pressure, half life and temperature. 

But how, having defined the half-life h/2 as the time necessary for half of a substance to decay or disappear, can we quantitatively determine the time elapsing since Otzi died In Justification Box 8.4, we show how the half-life and the rate constant of decay k are related according to... 

If one knows the half-life and amount remaining radioactive, you can then use equation (2) to calculate the rate constant, k, and then use equation (1) to solve for the time. This is the basis of carbon-14 dating. Scientists use carbon-14 dating to determine the age of objects that were once alive. 

PK For therapeutic range of 0.45. 5 tg/kg, maximum plasma concentration, half-life, and AUC are linear with respect to dose. Following subcutaneous injection, the absorption is slow and rate limiting. The half-life ranges from 27 to 89 hours. Peak plasma concentration is 34 hours after subcutaneous (SC) administration for CRF patients and 90 hours for cancer patients. 

Key AUC Area under the curve, Cmax maximal serum concentrations, Tmax time to reach peak concentrations, Vd volume distribution, K rate constant for elimination, T2 Elimination half-life, and CIT Total body clearance time. (Wojcicki et al. 1995)... 

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