COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
2nd Edition
ISBN: 9781319414597
Author: Freedman
Publisher: MAC HIGHER
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 27, Problem 25QAP
To determine
The number of radioactive atoms in a radioactive sample.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Nuclear Physics - Nuclear Structure
Density=
Nuclear Structure
Z
mass
Volume
radius
r=r04¹/3
ro=1.2x10-¹5 m
N
A = Z+N
4
The radius r of a nucleus is given in the above figure. The volume of a nucleus is V =
Proton
56 Fe nucleus has a total of 56 nucleons (protons + neutrons). The average mass of a nucleon is u = 1.66x10^-27 kg
I whin ber
Neutron
A
Z
If this unknown nucleus has 60 neutrons, how many protons does it have?
Enter a number
rr³
(a)Calculate the radius of a 56 Fe nucleus. Write the radius in fm, 1 fm = 10-15 m. Keep 2 decimal places.
Enter a number
x10-¹5m, fm
(b) Calculate the Denisity of a 56Fe nucleus.. Write the result in terms of 1017 kg/m³. Keep 2 decimal places.
Enter a number
x10¹7kg/m³
()
(c) An unknown hacieus has twice the volume of 56Fe. What is the mass number A of this nucleus?
Enter a number
i
The graph below shows the number of grams of a radioactive element t days after it was first discovered in
a science lab. Estimate the instantaneous rate of change of the number of grams of this object at 5 days.
+201
19
18
17
16
16
..
14
19
12
#
10
。
s
The numerical part of the instantaneous rate of change is
with units
For the units, enter full words. For example, if it was kph, you would say kilometers per hour. Or if it was
you would say meters per seconds squared.
m
2
8²
Growth of yeast cells In a controlled laboratory experiment,
yeast cells are grown in an automated cell culture system that
counts the number P of cells present at hourly intervals. The num-
ber after t hours is shown in the accompanying figure.
250
200
150
100
50
0 1 2 3 4 5 6 7
a. Explain what is meant by the derivative P'(5). What are its
units?
b. Which is larger, P'(2) or P'(3)? Give a reason for your
answer.
c. The quadratic curve capturing the trend of the data points
(see Section 1.4) is given by P(t) = 6.10r2 – 9.28t + 16.43.
Find the instantaneous rate of growth when t = 5 hours.
Chapter 27 Solutions
COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
Ch. 27 - Prob. 1QAPCh. 27 - Prob. 2QAPCh. 27 - Prob. 3QAPCh. 27 - Prob. 4QAPCh. 27 - Prob. 5QAPCh. 27 - Prob. 6QAPCh. 27 - Prob. 7QAPCh. 27 - Prob. 8QAPCh. 27 - Prob. 9QAPCh. 27 - Prob. 10QAP
Ch. 27 - Prob. 11QAPCh. 27 - Prob. 12QAPCh. 27 - Prob. 13QAPCh. 27 - Prob. 14QAPCh. 27 - Prob. 15QAPCh. 27 - Prob. 16QAPCh. 27 - Prob. 17QAPCh. 27 - Prob. 18QAPCh. 27 - Prob. 19QAPCh. 27 - Prob. 20QAPCh. 27 - Prob. 21QAPCh. 27 - Prob. 22QAPCh. 27 - Prob. 23QAPCh. 27 - Prob. 24QAPCh. 27 - Prob. 25QAPCh. 27 - Prob. 26QAPCh. 27 - Prob. 27QAPCh. 27 - Prob. 28QAPCh. 27 - Prob. 29QAPCh. 27 - Prob. 30QAPCh. 27 - Prob. 31QAPCh. 27 - Prob. 32QAPCh. 27 - Prob. 33QAPCh. 27 - Prob. 34QAPCh. 27 - Prob. 35QAPCh. 27 - Prob. 36QAPCh. 27 - Prob. 37QAPCh. 27 - Prob. 38QAPCh. 27 - Prob. 39QAPCh. 27 - Prob. 40QAPCh. 27 - Prob. 41QAPCh. 27 - Prob. 42QAPCh. 27 - Prob. 43QAPCh. 27 - Prob. 44QAPCh. 27 - Prob. 45QAPCh. 27 - Prob. 46QAPCh. 27 - Prob. 47QAPCh. 27 - Prob. 48QAPCh. 27 - Prob. 49QAPCh. 27 - Prob. 50QAPCh. 27 - Prob. 51QAPCh. 27 - Prob. 52QAPCh. 27 - Prob. 53QAPCh. 27 - Prob. 54QAPCh. 27 - Prob. 55QAPCh. 27 - Prob. 56QAPCh. 27 - Prob. 57QAPCh. 27 - Prob. 58QAPCh. 27 - Prob. 59QAPCh. 27 - Prob. 60QAPCh. 27 - Prob. 61QAPCh. 27 - Prob. 62QAPCh. 27 - Prob. 63QAPCh. 27 - Prob. 64QAPCh. 27 - Prob. 65QAPCh. 27 - Prob. 66QAPCh. 27 - Prob. 67QAPCh. 27 - Prob. 68QAPCh. 27 - Prob. 69QAPCh. 27 - Prob. 70QAPCh. 27 - Prob. 71QAPCh. 27 - Prob. 72QAPCh. 27 - Prob. 73QAPCh. 27 - Prob. 74QAPCh. 27 - Prob. 75QAPCh. 27 - Prob. 76QAPCh. 27 - Prob. 77QAPCh. 27 - Prob. 78QAPCh. 27 - Prob. 79QAPCh. 27 - Prob. 80QAPCh. 27 - Prob. 81QAPCh. 27 - Prob. 82QAPCh. 27 - Prob. 83QAPCh. 27 - Prob. 84QAPCh. 27 - Prob. 85QAPCh. 27 - Prob. 86QAPCh. 27 - Prob. 87QAPCh. 27 - Prob. 88QAPCh. 27 - Prob. 89QAPCh. 27 - Prob. 90QAPCh. 27 - Prob. 91QAPCh. 27 - Prob. 92QAPCh. 27 - Prob. 93QAPCh. 27 - Prob. 94QAPCh. 27 - Prob. 95QAPCh. 27 - Prob. 96QAPCh. 27 - Prob. 97QAP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- B. Carbon-14 is a radioactive isotope of carbon that has a half-life of 5600 years. It is used extensively in dating organic material that is tens of thousands of years old. Model the differential equation of the decay of the isotope if m is the mass and t is the time Calculate the constant using the half-life time. What fraction of the original amount of Carbon-14 in a sample would be present after 10,000 years? i) ii)arrow_forwardJohnny calculates from an experiment that he has 22 grams of carbon. However, he should have gotten 25 grams of carbon, which was the accepted value for this experiment. What was his percent error? •Remember: % Error =(EV-AV) x 100arrow_forwardThe rate of decay of the radioactive isotope Free Neutron 239 is given by: M = -1.1 x 10-³M where M is the mass of the isotope in grams and t is time measured in minutes. A sample initially contains 3 grams of the isotope. What is the mass of the isotope present in the sample after 320 minutes? The mass is grams. Round your answer to 3 significant figures, if needed. b) How long does it take for the mass of the isotope in the sample to fall to 1.5 gram? It takes t = minutes. Round your answer to the nearest integer if needed.arrow_forward
- A rock contains the radioactive isotope ? − 40 that decays with a half-life of 1.3 ??????? ????? and the radioactive isotope ?? − 87 that decays with a half-life of 48.6 ??????? ?????. The rock is 100 ??????? ????? old. The rock currently has 1000 times as many ?? − 87 atoms as there are ? − 40 atoms. (That is, ??? = 1000 × ??.) When the rock first formed it had ? times as many ?? − 87 atoms as ? − 40 atoms. (That is, ???,0 = ? × ??,0.) What is the value of ??arrow_forwardPart A Some atomic masses Particle Symbol Mass (u) Electron e 0.00055 Part B Proton р 1.00728 Neutron n 1.00866 Part C Hydrogen 'H 1.00783 Helium 4He 4.00260 Part D Calculate the mass defect of the helium nucleus He. The mass of neutral He is given by MHe = 4.002603 u. Express your answer in atomic mass units to three significant figures. · View Available Hint(s) ? uarrow_forwardConstruct Your Own Problem Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.arrow_forward
- How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10-22 s.arrow_forwardBacteria and other prokaryotes are found deep underground, in water, and in the air. One micron (106 m) is a typical length scale associated with these microbes. (a) Estimate the total number of bacteria and other prokaryotes in the biosphere of the Earth. (b) Estimate the total mass of all such microbes. (c) Discuss the relative importance of humans and microbes to the ecology of planet Earth. Can Homo sapiens survive without them?arrow_forwardOne can conceive an atomic nucleus, as a sphere charged uniformly, and positively. Let the proton number be Z; the charge in tensity of ei ther electron or proton is e =1.6x1019 Coulomb. Thereby the charge intensity of the nucleus athand, becomes Ze. Letits radius be R.arrow_forward
- Part A Some atomic masses Particle Symbol Mass (u) Electron e 0.00055 Part B Proton 1.00728 Neutron n 1.00866 Part C Hydrogen 1.00783 Helium 4 Не 4.00260 Part D Part E Calculate the binding energy EB of the helium nucleus He. Express your answer in megaelectron volts to three significant figures. • View Available Hint(s) EB = MeVarrow_forward*•58 Two radioactive materials that alpha decay, 238U and 232Th, and one that beta decays, "K, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the de- cay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotope 4"K has a single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information: Stable Decay Half-Life End Parent Mode (y) Point (MeV) (ppm) 238U 232Th 4.47 x 10° 206рЬ 51.7 1.41 x 1010 208Pb 42.7 13 1.28 x 10° 40Ca 1.31 4 In the table Q is the total energy released in the decay of one par- ent nucleus to the final stable end point and f is the abundance of the isotope in kilograms per kilogram of granite; ppm means parts per million. (a) Show that these materials produce energy as heat at the rate of 1.0 x 10-9 W for each kilogram of granite. (b) Assuming that there is 2.7 x 102 kg of granite in a 20-km-thick spherical shell at…arrow_forwardRADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 1010 Bq 1. Nuclear decay law: N = Noe-at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 1 and isotop half-life T1/2: 0.693 1= In(2) Radioisotope Half-life Modality T1/2 where å is decay constant (1/s), T1/2 is isotope half- life (s). T1/2 Carbon-11 20 minutes PET Fluorine-18 110 minutes PET Copper-64 12.7 hours PET 3. Activity or decay rate of a radioactive source A: Gallium-67 AN A = = AN 78.3 hours SPECT Gallium-68 68 minutes PET Technetum-99m 6.02 hours SPECT Δt where A is activity or decay rate of a radioactive source (Bq), N is number of nuclei present at time t Thallum-201 (s ), 2 is decay constant (1/s). 4. Activity A of a radioactive source at…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning