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In addition to chemical and biological systems, kinetic treatments can sometimes be applied to behavioral and social processes such as the evolution of technology. For example, in $1965,$ Gordon Moore, a co-founder of Intel, described a trend that the number of transistors on an integrated circuit ( $N$ ) roughly doubles every 1.5 yr. Now referred to as Moore's law, this trend has persisted for the past several decades. A plot of In $N$ versus year is shown here. (a) Determine the rate constant for the growth in the number of transistors on an integrated circuit.(b) Based on the rate constant, how long does it take for $N$ to double? (c) If Moore's law continues until the end of the century, what will be the number of transistors on an integrated circuit in the year $2100 ?$ Comment on your result.

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a. $$k=0.375 \mathrm{yr}^{-1}$$.b. $$1.85 \mathrm{yr}$$c. $7.7 \times 10^{23}$ transistors

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

University of Central Florida

University of Maryland - University College

Lectures

22:42

In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

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In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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Hello. So did I were going to be looking at, uh, this graph here where n is the number of transistors we've taken. The natural log of the trends is truce and we've plotted on the X axis are year and so we know we have the natural log of the number of transition stirs per year and you should notice this looks sort of like our first order reactions. We have sort of like the natural log of the the natural log of the reactant sort of here over time Onley you'll notice instead of being negative slope, it's a positive. So let's see if we can sort of treat this like, ah, almost reverse first order reaction. Well, in the first order reaction, the soap is negative in the slope is negative. K. So let's say that this is like a reaction. Well, we have here the slope. Let's say that the slope is okay. The positive k So how how do we approximate the slope Will will say that we've got natural log of n is five at around 1965 the natural given is about 10 at 1980. So we've got the natural log of 10 subtracting five over 1980 subtracting 1965. So that would just be five over. It's if 15. And that would be mean that the K would be zero 0.3 three in verse years. So for a Force first order reaction, we would have ah, half life, which would be given as the natural log of two over K. Well, this is sort of like the reverse. So we'll say that we have a doubling time will be equal to the natural log of to divided by K. So we will get by. Using this analogy, we will see that well, natural log of two, divided by 0.33 is 2.8 years. So let's say that we want to find out how Maney transistors they'll be in 2000 100. Well, if we say that in 1980 there was a natural log off n equals 10 that's the same thing is saying there were that end is equal to e to the 10th. So how about we use this doubling time so we've got E to the 10th and we have our doubling time. So if we were going to from 1980 to 2100. That's 120 years. And then we're going to divide that buyer doubling time to see how many times we're going to double. And so we will see if we do this math that we're going to have 5.2 times 10 to the 21st transistors in 2100 So there we go.

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