CEE 350 - Korshin - Winter 2012 - Homework 4(1)

# CEE 350 - Korshin - Winter 2012 - Homework 4(1) - CEE 350...

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1 CEE 350 Homework #4 Problem 1 (Textbook Problem 2.35, 0.3 points) What values of a and b would complete each of the following (X and Y are not meat to be any particular elements) Y X a b ± o D 266 88 Y X b a 32 15 ± o E This can be written as Y X 262 86 4 2 266 88 ± o Y X 32 16 32 15 ± o ² Problem 2 (Textbook Problem 3.11, 0.3 points) Bismuth-210 has a half-life of 4.85 days. If we start with 10 grams of it now, how much would we have left in 7 days? This can be easily calculated using the formula describing the radioactive decay ³´ g C t C t 68 . 3 2 10 2 85 . 4 7 0 2 / 1 u ² ² W Problem 3 (0.4 point) The figure below shows the decline of the abundance of 14 C after atmospheric nuclear explosions stopped in 1965. Using the data for 14 C since 1965, estimate the average half-life of atmospheric 14 C. Also determine the ratio of atmospheric removal rates and natural radioactive decay of 14 C (t 1/2 =5715 years). Figure HW4.1 Behavior of atmospheric 14 C in the period of time from 1940 to 1995.

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2 The profile of behavior of atmospheric 14 C is shown below. It can be seen that the time that corresponds to a 50% decline of 14 C after nuclear explosions in the atmosphere were stopped in 1965 occurred approximately between 1977 and 1978, so the half-life of atmospheric 14 C estimated based only on this point is 12.5 years. Figure HW4.2 Behavior of atmospheric 14 C in the period of time from 1940 to 1995. A more detailed analysis of the experimental data shown in the figure above (red dots) indicates that the data can be fit with an exponential function. The fitting of the data is shown in the figure below. It shows that the decay of atmospheric 14 C indeed follows an exponent and the kinetic constant is 0.0552 year -1 . The half-life estimated based on this more precise approach is 0.693/0.0552=12.55 years.
3 y = 0.9693e -0.0552x R 2 = 0.9977 0 0.2 0.4 0.6 0.8 1 1.2 05 1 0 1 5 2 0 2 5 3 0 Relative activity Expon. (Relative activity) Figure HW4.3 Behavior of relative activity of 14 C released as a result of atmospheric nuclear explosions as a function time elapsed after the tests were stopped. This is close to our first one-point estimate. Overall, the removal rate of atmospheric 14 C is much higher than its natural radioactive decay. The ratio of the rates is 5715/12.55=455.3. Problem 4 (Textbook Problem 3.5, 0.3 points) Suppose world carbon emissions are expressed as the following product: ±² population energy carbon person energy emissions Carbon u ¸ ¸ ¹ · ¨ ¨ © § u ¸ ¸ ¹ · ¨ ¨ © § _ If per capita energy demand increases at 1.5% per year, fossil fuel emissions of carbon per units of energy increase at 1% per year and world population grows at 1.5% per years, a. How long would it take before we are emitting carbon at twice the current rate? b. At that point, by what fraction would per capita energy demand have increased? c. At that point, by what fraction would total energy demand have increased?

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## This note was uploaded on 03/31/2012 for the course CEE 350 taught by Professor Korshin during the Spring '10 term at University of Washington.

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CEE 350 - Korshin - Winter 2012 - Homework 4(1) - CEE 350...

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