One method for determining the age of ancient objects is by radiocarbon dating. Natural processes convert nitrogen to Carbon-14, a radioactive isotope with a half-life of 5730 years. When they are alive, animals assimilate Carbon-14 through the food chain. When an animal dies, it stops replacing its carbon and the amount of Carbon-14 decays exponentially. (a) Suppose the minimum detectable amount is 0.1% of the initial amount. What is the maximum age of a fossil that we could date using Carbon-14? (b) Suppose we wanted to date a fossil that was potentially 70 million years old. A radioactive isotope with what half-life would be required?

One method for determining the age of ancient objects is by radiocarbon dating. Natural processes convert nitrogen to Carbon-14, a radioactive isotope with a half-life of 5730 years. When they are alive, animals assimilate Carbon-14 through the food chain. When an animal dies, it stops replacing its carbon and the amount of Carbon-14 decays exponentially. (a) Suppose the minimum detectable amount is 0.1% of the initial amount. What is the maximum age of a fossil that we could date using Carbon-14? (b) Suppose we wanted to date a fossil that was potentially 70 million years old. A radioactive isotope with what half-life would be required?

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter1: A Physics Toolkit

Section: Chapter Questions

Problem 1STP

See similar textbooks

Similar questions

Carbon-14 is an isotope of carbon that is formed when radiation from the sun strikes ordinary carbon dioxide in the atmosphere. Plants such as trees, which get their carbon dioxide from the atmosphere, therefore contain a small amount of carbon-14. Once a particular part of a plant has been formed, no more new carbon 14 is taken in. The carbon 14 in that part of the plant decays slowly. Let P be the percent of carbon-14 remaining in a part of a tree that grew t years ago (so t years ago, there was 100 percent of the carbon-14 existing in that part of the tree). Write the particular equation expressing P in terms of t. You may assume that the half-life of carbon-14 is 5730 years. a.) A piece of wood some believe to have come from Noah's Ark has 47.93% of its carbon-14 remaining. The Great Flood was supposed to have occurred in 4004 B.C. Is this piece of wood old enough to have come from Noah's Ark? Justify your answer. b.)
Suppose you are working as a reactor operator in the world’s largest nuclear power station at Kashiwazaki-Kariwa Nuclear Power Plant, Japan. The first unit in this station began to operate in 1985. Suppose the rate at which the nuclear power plant produces radioactive waste is proportional to the number of years it has been operating such that 500 pounds of waste is produced every year. Also, suppose that the waste decays exponentially at a rate of 5% per year. At the beginning of 2011, The Fukushima Daiichi nuclear disaster caused sever damages in the units which released the radiation waste to the atmosphere. Therefore, all the units were closed in 2011 for safety inspection. This left japan completely without nuclear-produced electrical power. Finally, the unit began to operate at the beginning of 2019. As a reactor operator, you are asked to do the following: a. Model the generation of the Kashiwazaki-Kariwa Nuclear Power Plant radioactive waste as a function of time. b.…
The radioactive gas krypton-85, produced by nuclear power plants as well as volcanoes, is present in trace amounts in earth’s atmosphere. Its half-life is 10.8 years. Suppose a volcano released 250 g of krypton-85 in an eruption. How much would remain after (a) 10.8 years, (b) 15 years, and (c) 50 years? Round to the nearest tenth of a gram.
A radioactive material disintegrate at such a rate that after 3.4 seconds, only 79% of the original substance is left. What is the half-life of the material, expressed in seconds (keep three significant digits)?
Phosphorus-32 has a half-life of 14.0 days. Starting with 8.00 g of 32P, how many grams will remain after 98.0 days ? Carbon-14 has a half-life of 5730 years. In a plant fossil, you find that the 14C has decayed to 1/16.0 of the original amount. How long ago was this plant alive?
Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32, in milligrams, is left from an original sample of 175 mg of Na "PO, after 38.8 days? Assume that the atomic mass of 32P is 32.0.
The rate of decay of a radioactive material is directly proportional to the amount of the material present, with the constant of proportional denoted by k. If the half-life of the material is 2.02 years, find k.
A radioactive element has a half-life of 3 days. The initial amount of that element is 1024 grams. How many grams of that element are left 12 days later? Write down your answer as an integer value (no decimals) and do not write the unit.
Iodine-131 is often used to treat Graves' disease or hyperthyroidism. In Graves' disease the thyroid begins to overproduce thyroid hormone. If a small amount of iodine-131 is consumed, it will concentrate in the thyroid gland and destroy its ability to function. If a tablet containing 15.0 μg of 131I is ingested by a patient, how many days will it take for the amount of iodine to decay to less than 1 μg?
The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) through (c) below. Year Death Rate 2000 256.6 (a) Find an exponential model of the form f(t) = y,b' for these data, where t= 0 2002 239.3 2004 218.0 210.9 corresponds to the year 2000. If you do not have suitable technology, use the first and last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function. 2006 2008 187.5 2010 178.2 171.2 165.0 2012 f(1) =DO' (Round to two decimal places as needed.) 2014
The half-life of phosphorus-32 is about 14days. There are 6.6 grams present initially.a. Express the amount of phosphorus-32 remaining as a function of time t.b. When will there be 1 gram remaining?
In a person infected with measles, the virus level N (measured in number of infected cells per ml of blood plasma) reaches a peak density at about t 12 days (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of N(t), the t-axis, and the lines t = 0 to t = 12, (as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells x time). N= f) 1000- 12 21 The function has been modeled by the function (t) = -t(t - 21)(t + 1). Use this model with six subintervals and their midpoints to estimate the total amount of infection (in (infected cells/mL) - day) needed to develop symptoms of measles.t (infected cells/mL) day Need Help? Read It