E c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where A is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ. ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.
E c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where A is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ. ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
![E
c)
For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where
A is the decay constant.
i)
Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ.
ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of
one gram of radium in Becquerels.
iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a
daughter product present will vary with time, Na(t). Sketch two graphs, with appropri-
ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0,
for the two extreme cases where the daughter product is much more radioactive than
the parent (\d >> \) and where the daughter product is much less radioactive than
the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which
graph is relevant and estimate the amount of radon in equilibrium with one mole of
radium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdd3134e-ea19-4bef-8e16-e6cc9083585d%2Fd7a4c565-8275-459e-bda0-18b69a975ea2%2F5mlsena_processed.jpeg&w=3840&q=75)
Transcribed Image Text:E
c)
For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where
A is the decay constant.
i)
Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ.
ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of
one gram of radium in Becquerels.
iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a
daughter product present will vary with time, Na(t). Sketch two graphs, with appropri-
ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0,
for the two extreme cases where the daughter product is much more radioactive than
the parent (\d >> \) and where the daughter product is much less radioactive than
the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which
graph is relevant and estimate the amount of radon in equilibrium with one mole of
radium.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 9 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
![College Physics: A Strategic Approach (4th Editio…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON