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Chapter 40: Problem 27

Write down equations to describe the \(\beta^{-}\) -decay of the following atoms: a) \({ }^{60} \mathrm{Co}\) b) \({ }^{3} \mathrm{H}\) c) \({ }^{14} \mathrm{C}\)

Short Answer

Expert verified
Question: Write down the equations for β− decay of Cobalt-60, Tritium, and Carbon-14. Answer: a) Cobalt-60: ${ }^{60}\mathrm{Co} \rightarrow { }^{60}\mathrm{Ni} + e^{-} + \bar{\nu_e}$ b) Tritium: ${ }^{3}\mathrm{H} \rightarrow { }^{3}\mathrm{He} + e^{-} + \bar{\nu_e}$ c) Carbon-14: ${ }^{14}\mathrm{C} \rightarrow { }^{14}\mathrm{N} + e^{-} + \bar{\nu_e}$

Step by step solution

01

Write the general equation for \(\beta^{-}\) decay

To begin with, we need to write a general equation for \(\beta^{-}\) decay. In this decay, a neutron (n) transforms into a proton (p), emitting an electron (e) and an electron-antineutrino (\(\bar{\nu}_e\)) in the process. This can be represented as: n \(\rightarrow\) p + e\(^{-}\) + \(\bar{\nu}_e\)
02

Write the provided isotopes in the form A ZX

In order to write the decay equations, we need first to express the given isotopes using the standard notation A ZX, where A is the mass number, Z is the atomic number, and X is the element symbol. a) \({ }^{60} \mathrm{Co}\) (Cobalt-60) b) \({ }^{3} \mathrm{H}\) (Tritium or Hydrogen-3) c) \({ }^{14} \mathrm{C}\) (Carbon-14)
03

Write the decay equations for each isotope

Now, we will write the decay equations for each isotope, applying the conservation of mass number and atomic number: a) \({ }^{60} \mathrm{Co}\) \(\rightarrow\) \({ }^{60} \mathrm{Ni}\) + e\(^{-}\) + \(\bar{\nu}_e\) b) \({ }^{3} \mathrm{H}\) \(\rightarrow\) \({ }^{3} \mathrm{He}\) + e\(^{-}\) + \(\bar{\nu}_e\) c) \({ }^{14} \mathrm{C}\) \(\rightarrow\) \({ }^{14} \mathrm{N}\) + e\(^{-}\) + \(\bar{\nu}_e\) These are the decay equations describing the \(\beta^{-}\) decay of Cobalt-60, Tritium, and Carbon-14.

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Most popular questions from this chapter

The mass of an atom (atomic mass) is equal to a) the sum of the masses of the protons. b) the sum of the masses of protons and neutrons. c) the sum of the masses of protons, neutrons and electrons. d) the sum of the masses of protons, neutrons, and electrons minus the atom's binding energy.

A certain radioactive isotope decays to one-eighth its original amount in \(5.00 \mathrm{~h} .\) How long would it take for \(10.0 \%\) of it to decay?

Using the table of isotopes in Appendix B, calculate the binding energies of the following nuclei. a) \({ }^{7} \mathrm{Li}\) b) \({ }^{12} \mathrm{C}\) c) \({ }^{56} \mathrm{Fe}\) d) \({ }^{85} \mathrm{Rb}\)

What is the average kinetic energy of protons at the center of a star where the temperature is \(1.00 \cdot 10^{7} \mathrm{~K} ?\) What is the average velocity of those protons?

The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms. a) Given the half-life of \({ }^{14} \mathrm{C}\) of \(5730 \mathrm{yr}\), calculate the specific activity of \({ }^{14} \mathrm{C}\). Express your result in disintegrations per second per gram, becquerel per gram, and curie per gram. b) Calculate the initial activity of a \(5.00-\mathrm{g}\) piece of wood. c) How many \({ }^{14} \mathrm{C}\) disintegrations have occurred in a \(5.00-\mathrm{g}\) piece of wood that was cut from a tree January \(1,1700 ?\)
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