A steady state plasma concentration is achieved in how many hours, if half life of drug is 40 hrs. ?
**Core Concept:**
The question is based on the concept of pharmacokinetics, specifically the relationship between drug half-life and time required to reach steady-state plasma concentration. Steady-state plasma concentration is the concentration of a drug that remains constant over time when administered repeatedly at a constant dose, while the body's ability to clear the drug and produce an effect remains constant. Half-life refers to the time required for the concentration of a drug to decrease to half its initial value.
**Why the Correct Answer is Right:**
The correct answer is determined by understanding the relationship between drug half-life and the time required to achieve steady-state plasma concentration. In this case, the drug has a half-life of 40 hours. To reach steady-state, the time it takes for the plasma concentration to decrease to half of its initial value should be equal to the drug's half-life. Therefore, the correct answer is 40 hours.
**Why Each Wrong Option is Incorrect:**
A) This option is incorrect because it does not match the relationship between half-life and time to reach steady-state.
B) This option is incorrect because it is double the time required to reach steady-state (40 hours / 2 = 20 hours).
C) This option is incorrect because it is triple the time required to reach steady-state (40 hours * 3 = 120 hours).
D) This option is incorrect because it is four times the time required to reach steady-state (40 hours * 4 = 160 hours).
**Why Each Wrong Option is Incorrect:**
A) In pharmacokinetics, the time required to reach steady-state is directly proportional to the drug's half-life. In this case, doubling the half-life (20 hours) would not result in a whole number (40 hours), making it incorrect.
B) Tripling the half-life (120 hours) is even longer than the actual time required for steady-state (40 hours), making it incorrect.
C) Quadrupling the half-life (160 hours) is even longer than the actual time required for steady-state (40 hours), making it incorrect.
D) Steady-state is achieved when the time taken to reach it equals the drug's half-life. Consequently, quadrupling the half-life (160 hours) is too long, making it incorrect.
**Clinical Pearl:**
Understanding the relationship between drug half-life and time to reach steady-state is crucial when prescribing medications. This concept helps optimize medication dosing and avoids potentially toxic or suboptimal drug concentrations.