Atoms consist of a nucleus made up of protons and neutrons. Orbiting outside the nucleus are a "cloud" of electrons. The number of protons determines the element. A carbon atom contains six protons and (normally)six neutrons; however, certain isotopes of carbon can exist. An isotope occurs when an atom has a different number of neutrons. Isotopes of carbon include: Carbon-12, Carbon-13, and Carbon-14.6 protons+ 6 neutronselectron+ protonneutronCarbon atomFigure 1: Depiction of a carbon atomCarbon is an element common in living (organic) matter with C-12 and C-14 occurring in similar abundances. These isotopes combine with Oxygen to form Carbon Dioxide which plants use in photosynthesis. Whenthese plants die, the C-12 and C-14 decay at different rates. (Radioactive decay occurs when an atom decays into a different element. Carbon-14 decays to Nitrogen-14.) Radiocarbon dating is a common techniqueused to find the age of dead organic matter by measuring the difference between C-12 and C-14 in a sample. This sample could be an ancient plant or animal. Use the C-14 curve below to answer the questions in thediscussion section.DataThe plot here represents the length of time between C-14 decays: X-Exp(A). Use this plot to answer the questions that follow.0.000125f(0) = 0.0001210.0001000.0000750.0000500.0000250.00000010,00020,00030,00040,00050,000Figure 2: Probability of decay Given that a C-14 atom has not decayed for 6,500 years, what is the probability that it will decay after 7,000 years?P(X > 7000|X> 6500)Round your answer to four decimal places.

X ~ Exp(λ) So, PDF of X is given by, f(x) = 1λe-xλ , x>0 Given, f(0) = 0.000121 So, we get,…

Answered: Given that a C-14 atom has not decayed…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Given that a C-14 atom has not decayed for 6,500 years, what is the probability that it will decay after 7,000 years? P(X > 7000| X > 6500) Round your answer to four decimal places.