a) Calculate the speeds of the electrons from a 1 kV electron gun and from a 1 MV electron gun. The mass of the electron is 0.511 MeV. or 9.109 × 10- kg. -31 [5 marks] b) The resistance R of a conductor depends on its shape and physical dimensions and a property of the material called the resistivity p. i) What does the resistivity of a material depend upon? ii) Assuming that the resistivity of copper is a quarter of that of aluminium and that the density of copper is three times that of aluminimium, find the ratio of the masses of copper and aluminium wires with the same length and the same resistance but with different cross-sectional areas. [10 marks] c) For a radio-nuclide, a number No of atoms at time t \ is the decay constant. = 0 decays as N(t) = No ext, where i) Derive the relationship between the half-life t½ and the time constant T = 1/λ. 2 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 (\ɑ << 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.
a) Calculate the speeds of the electrons from a 1 kV electron gun and from a 1 MV electron gun. The mass of the electron is 0.511 MeV. or 9.109 × 10- kg. -31 [5 marks] b) The resistance R of a conductor depends on its shape and physical dimensions and a property of the material called the resistivity p. i) What does the resistivity of a material depend upon? ii) Assuming that the resistivity of copper is a quarter of that of aluminium and that the density of copper is three times that of aluminimium, find the ratio of the masses of copper and aluminium wires with the same length and the same resistance but with different cross-sectional areas. [10 marks] c) For a radio-nuclide, a number No of atoms at time t \ is the decay constant. = 0 decays as N(t) = No ext, where i) Derive the relationship between the half-life t½ and the time constant T = 1/λ. 2 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 (\ɑ << 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.
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter21: Current And Direct Current Circuits
Section: Chapter Questions
Problem 16P
Related questions
Question
![a) Calculate the speeds of the electrons from a 1 kV electron gun and from a 1 MV electron
gun. The mass of the electron is 0.511 MeV. or 9.109 × 10- kg.
-31
[5 marks]
b) The resistance R of a conductor depends on its shape and physical dimensions and a
property of the material called the resistivity p.
i) What does the resistivity of a material depend upon?
ii)
Assuming that the resistivity of copper is a quarter of that of aluminium and that the
density of copper is three times that of aluminimium, find the ratio of the masses of
copper and aluminium wires with the same length and the same resistance but with
different cross-sectional areas.
[10 marks]
c)
For a radio-nuclide, a number No of atoms at time t
\ is the decay constant.
=
0 decays as N(t) = No ext, where
i)
Derive the relationship between the half-life t½ and the time constant T = 1/λ.
2
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 (\ɑ << 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%2Fff7d6b45-4f61-46c6-8aba-0dc1374a8217%2Fc05f79c2-5859-4515-b022-7765123e31a0%2Fnc8np6a_processed.png&w=3840&q=75)
Transcribed Image Text:a) Calculate the speeds of the electrons from a 1 kV electron gun and from a 1 MV electron
gun. The mass of the electron is 0.511 MeV. or 9.109 × 10- kg.
-31
[5 marks]
b) The resistance R of a conductor depends on its shape and physical dimensions and a
property of the material called the resistivity p.
i) What does the resistivity of a material depend upon?
ii)
Assuming that the resistivity of copper is a quarter of that of aluminium and that the
density of copper is three times that of aluminimium, find the ratio of the masses of
copper and aluminium wires with the same length and the same resistance but with
different cross-sectional areas.
[10 marks]
c)
For a radio-nuclide, a number No of atoms at time t
\ is the decay constant.
=
0 decays as N(t) = No ext, where
i)
Derive the relationship between the half-life t½ and the time constant T = 1/λ.
2
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 (\ɑ << 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.
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